




























































































































































































# 




\ 






SUMMARY TECHNICAL REPORT 
OF THE* 

NATIONAL DEFENSE RESEARCH COMMITTEE 


Manuscript and illustrations for this volume were prepared for 
publication by the Summary Reports Group of the Columbia 
University Division of War Research under contract OEMsr-1131 
with the Office of Scientific Research and Development. This vol¬ 
ume was printed and bound by the Columbia University Press. 

Distribution of the Summary Technical Report of NDRC has 
been made by the War and Navy Departments. Inquiries concern¬ 
ing the availability and distribution of the Summary Technical 
Report volumes and microfilmed and other reference material 
should be addressed to the War Department Library, Room 
1A-522, The Pentagon, Washington 25, D. C., or to the Office of 
Naval Research, Navy Department, Attention: Reports and 
Documents Section, Washington 25, D. C. 

Copy No. 

V “ 3 

This volume, like the seventy others of the Summary Technical 
Report of NDRC, has been written, edited, and printed under 
great pressure. Inevitably there are errors which have slipped past 
Division readers and proofreaders. There may be errors of fact not 
known at time of printing. The author has not been able to follow 
through his writing to the final page proof. 

Please report errors to: 

JOINT RESEARCH AND DEVELOPMENT BOARD 
PROGRAMS DIVISION (STR ERRATA) 

WASHINGTON 25, D. C. 

A master errata sheet will be compiled from these reports and sent 
to recipients of the volume. Your help will make this book more 
useful to other readers and will be of great value in preparing any 
revisions. 


SUMMARY TECHNICAL REPORT OF THE 
COMMITTEE ON PROPAGATION, NDRC 
VOLUME 1 


HISTORICAL AND 
TECHNICAL SURVEY 


OFFICE OF SCIENTIFIC RESEARCH AND DEVELOPMENT 
VANNEVAR BUSH, DIRECTOR 

NATIONAL DEFENSE RESEARCH COMMITTEE 
JAMES B. CONANT, CHAIRMAN 

COMMITTEE ON PROPAGATION 
CHAS. R. BURROWS, CHAIRMAN 


v • ,.t 


WASHINGTON, D. C., 1946 



NATIONAL DEFENSE RESEARCH COMMITTEE 


a -JAN12 



James B. Conant, Chairman 
Richard C. Tolman, Vice Chairman 
Roger Adams Army Representative 1 

Frank B. Jewett Navy Representative 2 

Karl T. Compton Commissioner of Patents 3 

Irvin Stewart, Executive Secretary 


l Army Representatives in order of service: 

Maj. Gen. G. V. Strong Col. L. A. Denson 

Maj. Gen. R. C. Moore Col. P. R. Faymonville 

Maj. Gen. C. C. Williams Brig. Gen. E. A. Regnier 

Brig. Gen. W. A. Wood, Jr. Col. M. M. Irvine 

Col. E. A. Routheau 


2 Navy Representatives in order of service: 

Rear Adm. H. G. Bowen Rear Adm. J. A. Furer 

Capt. Lybrand P. Smith Rear Adm. A. H. Van Keuren 

Commodore H. A. Schade 
3 Commissioners of Patents in order of service: 

Conway P. Coe Casper W. Ooms 


NOTES ON THE ORGANIZATION OF NDRC 


The duties of the National Defense Research Committee 
were (1) to recommend to the Director of OSRD suitable 
projects and research programs on the instrumentalities of 
warfare, together w r ith contract facilities for carrying out 
these projects and programs, and (2) to administer the tech¬ 
nical and scientific work of the contracts. More specifically, 
NDRC functioned by initiating research projects on requests 
from the Army or the Navy, or on requests from an allied 
government transmitted through the Liaison Office of OSRD, 
or on its own considered initiative as a result of the experi¬ 
ence of its members. Proposals prepared by the Division, 
Panel, or Committee for research contracts for performance 
of the work involved in such projects were first reviewed by 
NDRC, and if approved, recommended to the Director of 
OSRD. Upon approval of a proposal by the Director, a con¬ 
tract permitting maximum flexibility of scientific effort was 
arranged. The business aspects of the contract, including 
such matters as materials, clearances, vouchers, patents, 
priorities, legal matters, and administration of patent matters 
were handled by the Executive Secretary of OSRD. 

Originally NDRC administered its work through five 
divisions, each headed by one of the NDRC members. 
These were: 

Division A—Armor *and Ordance 

Division B—Bombs, Fuels, Gases, & Chemical Problems 
Division C—Communication and Transportation 
Division D—Detection, Controls, and Instruments 
Division E—Patents and Inventions 


In a reorganization in the fall of 1942, twenty-three ad¬ 
ministrative divisions, panels, or committees were created, 
each with a chief selected on the basis of his outstanding 
work in the particular field. The NDRC members then be¬ 
came a reviewing and advisory group to the Director of 
OSRD. The final organization was as follows: 

Division 1—Ballistic Research 

Division 2—Effects of Impact and Explosion 

Division 3—Rocket Ordinance 

Division 4—Ordnance Accessories 

Division 5—New Missiles 

Division 6—Sub-Surface Warfare 

Division 7—Fire Control 

Division 8—Explosives 

Division 9—Chemistry 

Division 10—Absorbents and Aerosols 

Division 11—Chemical Engineering 

Division 12—Transportation 

Division 13—Electrical Communication 

Division 14—Radar 

Division 15—Radio Coordination 

Division 16—Optics and Camouflage 

Division 17—Physics 

Division 18—War Metallurgy 

Division 19—Miscellaneous 

Applied Mathematics Panel 

Applied Psychology Panel 

Committee on Propagation 

Tropical Deterioration Administrative Committee 


IV 






NDRC FOREWORD 


As events of the years preceding 1940 revealed 
more and more clearly the seriousness of the 
world situation, many scientists in this country came 
to realize the need of organizing scientific research 
for service in a national emergency. Recommenda¬ 
tions which they made to the White House were 
given careful and sympathetic attention, and as a 
result the National Defense Research Committee 
(NDRC) was formed by Executive Order of the 
President in the summer of 1940. The members of 
NDRC, appointed by the President, were instructed 
to supplement the work of the Army and the Navy 
in the development of the instrumentalities of war. 
A year later, upon the establishment of the Office 
of Scientific Research and Development [OSRD], 
NDRC became one of its units. 

The Summary Technical Report of NDRC is a 
conscientious effort on the part of NDRC to sum¬ 
marize and evaluate its work and to present it in a 
useful and permanent form. It comprises some 
seventy volumes broken into groups corresponding 
to the NDRC Divisions, Panels, and Committees. 

The Summary Technical Report of each Division, 
Panel, or Committee is an integral survey of the work 
of that group. The first volume of each group’s report 
contains a summary of the report, stating the prob¬ 
lems presented and the philosophy of attacking them, 
and summarizing the results of the research, develop¬ 
ment, and training activities undertaken. Some vol¬ 
umes may be “state of the art” treatises covering 
subjects to which various research groups have con¬ 
tributed information. Others may contain descrip¬ 
tions of devices developed in the laboratories. A 
master index of all these divisional, panel, and com¬ 
mittee reports which together constitute the Sum¬ 
mary Technical Report of NDRC is contained in a 
separate volume, which also includes the index of a 
microfilm record of pertinent technical laboratory 
reports and reference material. 

Some of the NDRC-sponsored researches which 
had been declassified by the end of 1945 were of 
sufficient popular interest that it was found desirable 
to report them in the form of monographs, such as 
the series on radar by Division 14 and the monograph 
on sampling inspection by the Applied Mathematics 
Panel. Since the material treated in them is not 


duplicated in the Summary Technical Report of 
NDRC, the monographs are an important part of 
the story of these aspects of NDRC research. 

In contrast to the information on radar, which is of 
widespread interest and much of which is released to 
the public, the research on subsurface warfare is 
largely classified and is of general interest to a more 
restricted group. As a consequence, the report of 
Division 6 is found almost entirely in its Summary 
Technical Report, which runs to over twenty vol¬ 
umes. The extent of the work of a division cannot 
therefore be judged solely by the number of volumes 
devoted to it in the Summary Technical Report of 
NDRC; account must be taken of the monographs 
and available.reports published elsewhere. 

Though the Committee on Propagation had a com¬ 
paratively short existence, being organized rather 
late in the war program, its accomplishments were 
definitely effective. That so many individuals and 
organizations worked together so harmoniously and 
contributed so willingly to the Committee’s efforts 
is a tribute to the leadership of the Chairman, Chas. 
R. Burrows. The^atest information in this field was 
gathered from the four corners of the earth, organ¬ 
ized, and dispatched to the points where it would aid 
most in the prosecution of the war. 

Much credit must be given, not only to the mem¬ 
bers of the Committee and its contractors, but also 
to the many other individuals who gave so generously 
of their time and effort. This group included a num¬ 
ber of our Canadian and British allies. In addition to 
the assistance given the war effort, a considerable 
contribution has been made to the knowledge of 
short-wave transmission and especially to the inter¬ 
relation of this phenomenon with meteorological con¬ 
ditions. Such information will be most valuable in 
weather forecasting and in furthering the usefulness 
of the whole radio field. 

Yannevar Bush, Director 
Office of Scientific Research and Development 

J. B. Conant, Chairman 
National Defense Research Committee 























































































































* 





































































FOREWORD 


T he success of the propagation program was the 
result of the wholehearted cooperation of many 
individuals in the various organizations concerned, 
not only in this country but in England, Canada, 
New Zealand, and Australia. The magnitude of the 
research work accomplished was possible only because 
of the willingness of the workers in many organiza¬ 
tions to undertake their parts of the overall program. 
In fact, the entire program of the Committee on 
Propagation was carried out without the necessity 
of the Committee exercising directive authority over 
any project. 

Dr. Hubert Hopkins of the National Physical 
Laboratory in England and Mr. Donald E. Kerr of 
the Radiation Laboratory at the Massachusetts 
Institute of Technology, who were working on this 
phase of the war effort when the Propagation Com¬ 
mittee was formed, were instrumental in giving a 
good start to its activities. The largest single group 
working for the Committee was under Mr. Kerr. 

The existence of a common program for the united 
nations in radio wave propagation resulted from the 
splendid cooperation given the Propagation Mission 
to England by Sir Edward Appleton and his Ultra 
Short Wave Panel. Later, through the cooperation 
of Canadian engineers and scientists, Dr. W. R. 
McKinley of the National Research Council of 
Canada and Dr. Andrew Thomson of the Air Services 
Meteorological Division, Department of Transport, 
Toronto, Canada, undertook to carry on a part of the 
program originally assigned to the United States. 
The program was further rounded out by the willing¬ 
ness of the New Zealand government to undertake 
an experiment for which their situation was particu¬ 
larly favorable. Dr. F. E. S. Alexander of New 
Zealand and Dr. Paul A. Anderson of the State 
College of Washington initiated this work. Needless 
to say/jthe labor of the Committee on Propagation 
could hardly have been effective without the coopera¬ 
tion of the Army and Navy. Maj. Gen. H. M. 
McClelland personally established Army coopera¬ 


tion, and Lt. Comdr. Ralph A. Krause and Capt. 
Lloyd Berkner were similarly helpful in organizing 
Navy liaison and help. 

Officers and scientific workers of the U. S. Navy 
Radio and Sound Laboratory at San Diego, Califor¬ 
nia, altered their program on propagation to fit in 
with the overall program of the Committee. Capt. 
David R. Hull, Bureau of Ships, understanding the 
importance of the technical problems, paved the way 
for effective cooperation by this laboratory. 

Dr. Ralph Bown, Radio and Television Research 
Director, Bell Telephone Laboratories, integrated the 
research program undertaken by Bell Telephone 
Laboratories for the Committee on Propagation. 
This joint research program included meteorological 
measurements on Bell Telephone Laboratories prop¬ 
erty by meterologists of the Army Air Forces work¬ 
ing with Col. D. N. Yates, Director, and Lt. Col. 
Harry Wexler of the Weather Wing, Army Air Forces. 
The accomplishments of the Committee on Propaga¬ 
tion are a good example of the effectiveness of co¬ 
operation-all parts were essential and none more 
than the rest. 

I want to thank Dr. Karl T. Compton, President 
of the Massachusetts Institute of Technology, who 
was always willing to discuss problems of the Com¬ 
mittee and who helped me to solve many of the more 
difficult ones, and also, Prof. S. S. Attwood, Univer¬ 
sity of Michigan, whose continual counsel through¬ 
out my term of office was in no small way responsible 
for the success of our activity. 

Credit is also due Bell Telephone Laboratories, 
which made my services available to the government 
and paid my salary from August 1943 to September 
1945, and to Cornell University, which has allowed 
me time off with pay to complete the work of the 
Committee on Propagation since September 1945. 

Chas. R. Burrows 
Chairman, Committee on Propagation 


vii 















































































































































































































































































• • 




/ 















































PREFACE 


I n this series of three volumes, which is part of the 
Summary Technical Report of NDRC, the Com¬ 
mittee on Propagation is presenting a record of its 
activities and technical developments. The material 
presented, concerning as it does the propagation of 
radio waves through the troposphere, is of permanent 
value both in war and in peace. 

The present volume is divided into four parts. 
Part I outlines the organization and activities of the 
NDRC Committee on Propagation, gives the mecha¬ 
nism used for coordinating the various Service and 
civilian organizations interested in propagation, and 
makes recommendations for continued activity in 
studying propagation phenomena. 

Part II gives a critical overall view of the technical 
developments in the study of tropospheric propaga¬ 
tion. Outlined is the general theory of both standard 
and nonstandard propagation together with descrip¬ 
tions and results of transmission experiments carried 
out in widely separated parts of the earth and de¬ 
signed to test the theory. Included also is a resume 
of the meteorological factors affecting propagation 
of waves and their attenuation in the atmosphere. 

The second, third, and fourth Conferences on 
Propagation, under the auspices of the NDRC Com¬ 
mittee on Propagation, were held in February 1944, 


November 1944, and May 1945, respectively. The 
bulk of the technical material presented at the con¬ 
ferences is published in Volume 2 of this series and in 
Part III and Part IV of the present volume. These 
comprise the material dealing with the theory of both 
standard and nonstandard propagation. Certain re¬ 
ports have been omitted, primarily because the 
material was superseded by later studies or is covered 
adequately elsewhere. 

The General Bibliography lists reports on tropo¬ 
spheric propagation issued by numerous Service and 
civilian organizations of both the United States and 
the British Empire. With a few exceptions, original 
reports listed in the Bibliography for this volume 
have been microfilmed. A few, such as summary 
reports issued by the Columbia University Wave 
Propagation Group and the compiled Propagation 
Conference Reports, are included in the present series. 

Acknowledgment is due to the many authors who 
have contributed to this series, not only for the 
material and its oral presentation at the conferences, 
but also for their willingness to prepare the material 
in form for permanent record. 

Stephen S. Attwood 
Editor 


ix 






CONTENTS 

CHAPTER 

PAGE 

Summary. 1 

PART I 
HISTORY 

1 Origin and Organization... 5 

2 Objectives and Research Agencies. 9 

3 Chronological Record. 13 

4 Results and Recommendations. 25 

PART II 
SUMMARY 

5 Standard Propagation. 31 

6 Elementary Theory of Nonstandard Propagation. 42 

7 Meteorological Measurements. 50 

8 Transmission Experiments. 58 

9 General Meteorology and Forecasting. 75 

10 Scattering and Absorption of Microwaves. 82 

PART III 

CONFERENCE REPORTS ON STANDARD 
PROPAGATION 

11 A Graphical Method for the Determination of Standard 

Coverage Charts. 93 

12 Nomographic Solutions for the Standard Case. 95 

13 Theoretical Analysis of Errors in Radar Due to 

Atmospheric Refraction.106 

14 Diffraction of Radio Waves over Hills.110 

15 Siting and Coverage of Ground Radars.113 

16 Variations in Radio Coverage.178 


XI 



















Xll 


CONTENTS 


CHAPTER PAGE 

PART IV 

CONFERENCE REPORTS ON NONSTANDARD 
PROPAGATION 

17 Tropospheric Propagation and Radio Meteorology.189 

18 Theoretical Treatment of Nonstandard Propagation in the 

Diffraction Zone.226 

19 Characteristic Values for the First Mode for the Bilinear 

M Curve.. 228 

20 Incipient Leakage in a Surface Duct.233 

21 The Solution of the Propagation Equation in Terms of 

Hankel Functions.237 

22 Attenuation Diagrams for Surface Ducts.240 

23 Approximate Analysis of Guided Propagation in a 

Nonhomogeneous Atmosphere.244 

24 Some Theoretical Results on Nonstandard Propagation. . .247 

25 Perturbation Theory for an Exponential M Curve in 

Nonstandard Propagation.249 

26 First Order Estimation of Radar Ranges over the Open 

Ocean.256 

27 Convergence Effects in Reflections fromTropospheric 

Layers.258 

Bibliography—Volume 1.261 

General Bibliography.277 

OSRD Appointees.310 

Contracts.311 

Service Projects.312 

Index.313 



















INTRODUCTION 


T his report is a summary of the activities of 
the Committee on Propagation, NDRC. It is 
divided into three parts, each of which deals with a 
particular type of activity or record. 

Part I is an account of the administrative activities 
of the Committee, its origin, organization, and work, 
with a description of the needs of the armed forces 
which called it into being. It is divided into four 
chapters for convenient reference. In general, the 
technical aspects of the problems set before the 
Committee, and of the work undertaken to solve 
those problems, are touched on in Part I only suffi¬ 
ciently to make clear the needs of the Services and 
the steps taken to satisfy those needs. Actual 
chronology is adhered to as far as possible with any 
departures indicated where they occur. This part of 
the report is designed to serve not only as a record 
of the Committee's work but to assist any future 
group in the organization of a similar program, 
should the occasion arise. Chapters 1 and 2 describe 
the organizational setup, liaison channels, objectives, 
the changes which occurred, and the reasons for 
making them. Chapter 3 relates the chronological 
activities of the organization. Chapter 4 summarizes 
the results accomplished and also contains a critique 
of the organization and its work, as evaluated by the 
chairman, with recommendations for future investi¬ 
gation in this field. 

Part II is a technical description of the develop¬ 
ment of propagation work during W >rld W ir II and 
the results obtained by the various organizations 
engaged in this work. Chapter 5 begins with a defi¬ 
nition of certain basic concepts and proceeds with a 
review of so-called standard propagation as known 
at the beginning of the war. For a rapid survey 
of the vast body of information that has since been 
acquired, Chapter 6 reviews nonstandard propaga¬ 
tion from an elementary theoretical viewpoint. The 
principal discovery made during the war is that the 
effective range of radar and short-wave radio equip¬ 
ment depends essentially and critically on the 
distribution of the refractive index in the lower 
strata of the atmosphere. In Chapter 7 the newly 
developed methods for the measurement of the 
refractive index variation are described, and a collec¬ 
tion of typical refractive index curves resulting from 
actual measurements in various parts of the world 
is presented. 

Chapter 8, the central chapter of Part II, gives a 
brief chronological record and the principal results of 


the major propagation experiments performed in 
Great Britain, Canada, and the United States. 
Because short and microwave propagation charac¬ 
teristics are determined by the physicial condition 
of the lower atmosphere, they are intimately 
connected with the evolution of the weather on a 
large scale as studied by the forecasting meteorolo¬ 
gist. The relationships between the dynamics of 
the air and the distribution of refractive index are 
presented in Chapter 9. A review of the climatic 
and seasonal conditions involved in various parts of 
the world and of the bearing of all these factors upon 
the forecasting of radio propagation conditions is 
included. Finally, in Chapter 10, the results of 
investigations on the atmospheric absorption of 
microwaves and of the scattering of short and 
microwaves by radar targets and by raindrops are 
summarized. 

The data given in this report refer only to the 
transmission of the higher frequency bands, above 
about 30 me. 

Parts III and IV are devoted to the presentation of 
18 reports, out of 61 published in the Summary 
Technical Report, which were presented before the 
second, third and fourth conferences on propagation 
held in February, 1944, November 1944, and May 
1945, or were published by the Columbia University 
Wave Propagation Group. Those appearing in Chap¬ 
ters 11 through 15 are concerned with standard 
propagation; Chapters 16 through 27 with nonstand¬ 
ard propagation. The remaining 43 reports are pub¬ 
lished in Volume 2. 

One of the main functions of the Committee was 
to bring about a rapid exchange of information 
between the laboratories and Service units working 
on the subject, thus making the results available to 
all workers technically concerned with the military 
application of radar and other short wave radio 
equipment. To fulfill this function the Columbia 
University W ive Propagation Group operating under 
contract with the Committee periodically published 
a comprehensive bibliqgraphy on propagation, begin¬ 
ning in the spring of 1944. Its fifth and last edition, 
issued in August 1945, is included in this volume. 
This bibliography is a rather exhaustive documenta¬ 
tion of the efforts made during the war in this field 
by Great Britain, Canada, New Zealand, Australia, 
and the United States. Reference to papers and 
reports is made in the main body of this summary 
by superior numbers. 


1 




































' 























































































































































‘ 


















PART I 


HISTORY 











Chapter 1 

ORIGIN AND ORGANIZATION 


11 ORIGIN 

I n august 1943, Dr. K. T. Compton, a member 
of the National Defense Research Committee 
[NDRC], in the course of discharging his duties 
resulting from his “radar mission” to England, asked 
Dr. Chas. R. Burrows of the Bell Telephone Labora¬ 
tories if he would undertake the coordination of 
research work on radio wave propagation in the 
United States under the auspices of NDRC. This 
was the initial step in the formation of the Committee 
on Propagation. During the Compton radar mission 
the urgent need for radar information in the armed 
forces was discussed by Dr. Compton and Sir Ed¬ 
ward Appleton. 

The Committee on Propagation of the National 
Defense Research Committee was organized in 
August 1943, under the chairmanship of Dr. Burrows. 
This body was created for the purpose of coordinating 
American scientific investigation of the propagation 
of electromagnetic waves through the lower atmos¬ 
phere (troposphere), correlating the United States 
research with that being carried out in Great Britain 
and other countries of the United Nations and trans¬ 
mitting the information obtained to the Armed 
Forces in usable form, as speedily as possible. 

It was decided that the propagation phenomena 
referred to could be divided into two classes: one, 
the effects of the troposphere itself on electromag¬ 
netic radiation of the wavelengths under discussion 
and, two, the effects of the earth’s land and water 
surfaces in reflecting radiation incident at various 
angles. A British memorandum dated April 28, 1943 
was drawn up, inviting specific United States cooper¬ 
ation in investigation of the following problems: 

1. The entire question of effects of tropospheric 
conditions near and over a continental land mass 
similar in size, climate, and topography to Europe, 
on radiation of radar frequencies, in meteorological 
environments ranging from polar to tropical, with 
particular emphasis on obtaining quantitative data. 
British facilities and environments for this investi¬ 
gation were limited. 

2. An exhaustive study of propagation under 
desert and moist tropical conditions, particular^ 
with transmitter and receiver at heights of less 
than 100 ft. 


3. Propagation under temperate climatic condi¬ 
tions with either the receiver or transmitter at heights 
from 5,000 to 10,000 ft. 

4. Experiments to determine the dependence of 
the reflection coefficient on the ang e of incidence 
with the surface of a rough sea. 

5. Experiments along nearly optical paths over 
various kinds of topography likely to be encountered 
in field operations. Exhaustive knowledge of this 
aspect of the general propagation problem appeared 
to be an urgent necessity, and comparison of United 
States and United Kingdom experience was con¬ 
sidered highly desirable. 

It was felt that such investigations, correlated 
with parallel work on those aspects of the research 
which could be carried out in Great Britain, would 
produce early results of great importance to the 
successful prosecution of the war. 

It was extremely important for the armed forces 
to know with reasonable accuracy the coverage to 
be expected with given radar or radio communica¬ 
tion equipment under various conditions of terrain 
and meteorology. In order that this coverage could 
be determined it was necessary to know the laws 
governing electromagnetic wave propagation, and 
these laws could be derived only by an extensive 
theoretical and experimental research program. The 
urgency and importance of the entire matter of cover¬ 
age become obvious when the following pertinent 
aspects of modern warfare are considered: 

1. The development of highly mobile and powerful 
instruments (such as the improved tank and other 
surface combat vehicles, and of long range, high 
speed bombardment aircraft employed for strategic 
attacks on the means of production and civilian 
morale, as well as for tactical purposes) which per¬ 
mitted the principal belligerents to readopt a war 
of movement, instead of one of static fortification 
and attrition, and made the development of devices 
for detecting the presence and movements of enemy 
mobile units vitally necessary. 

2. The necessity of protecting extremely extended 
sea and land supply lines from successful attack by 
enemies who early realized that their major hope of 
ultimate victory lay in cutting those lines. 

3. The enormous extent and diversity of the 
various theaters of operations, necessitating inte- 

5 


6 


ORIGIN AND ORGANIZATION 


grated global communications over vast areas of 
unfavorable terrain and with thousands of mobile 
units. 

Very early in the conflict it was realized that only 
the British development and organized employment 
of radar had permitted that country, with a numeric¬ 
ally inferior air force, to defeat the Luftwaffe deci¬ 
sively in the Battle of Britain, in which the German 
High Command had hoped to destroy the Royal 
Air Force and open the way for a successful invasion 
of Great Britain. Early warning radar permitted the 
British commanders to conserve their small resources 
of men and materiel by sharply reducing air patrol¬ 
ling, and by conducting interceptions with an exac¬ 
titude which conserved men and aircraft flying hours 
to the utmost. 

With the importance of radar thus established, its 
use was rapidly expanded and extended into new 
applications. To protect the extremely long sea 
supply lines from crippling submarine attacks, radar 
detection devices were developed expressly to detect 
surfaced submarines as the only practicable means 
of searching wide areas of ocean under varying 
conditions. 

With the entry of the Japanese into the struggle, 
the field of operations became truly global, and the 
demands made on detection and communication 
equipment became more severe in all respects. Rapid 
improvement was made in the performance and 
reliability of radio and radar equipment to meet 
these increased demands. 

With these advances in design and manufacture 
and the speedy accumulation of a large amount of 
factual data on equipment performance in the field, 
it soon became apparent that meteorological condi¬ 
tions in the troposphere had very serious influence 
on the operational efficiency of such apparatus. In 
particular, it was noted that the reliable coverage 
area of a given installation varied considerably with 
weather conditions, with the result that confidence 
in early warning radar and very high-frequency 
communication links was reduced, and this loss of 
confidence affected field operations seriously. It thus 
became vitally necessary to investigate as rapidly 
and completely as practicable the causes of such 
variations, with a view to discovering ways of mini¬ 
mizing reductions of coverage and reliability and to 
improving the general overall performance. 

The need for this investigation was communicated 
from units in the field through regular liaison channels 
to the National Defense Research Committee 


[NDRC] in the United States, and to the Depart¬ 
ment of Scientific and Industrial Research in Great 
Britain. Certain researches into the problem were 
begun independently in the two countries. During 
the course of the discussion perviously referred to 
between Dr. Compton and Sir Edward Appleton, 
the need for a body to coordinate these researches 
was revealed. The magnitude and complexity of 
the problem, occasioned by the extreme variations 
in equipment, siting, terrain, and meteorology in 
the various theaters of operations, made it essential 
to divide the investigation so as to avoid gaps 
or duplication of effort. This could be achieved 
only by integrating research programs through a 
coordinating body. 

Accordingly the radar mission under the chairman¬ 
ship of Dr. Compton, upon its return to the United 
States strongly recommended the formation of such 
a body. 

12 ORGANIZATION 

A preliminary conference on propagation was held 
July 1 and 2, 1943 at the Massachusetts Institute of 
Technology, at which most of the interested United 
States agencies were represented. This conference 
was held under the chairmanship of Donald E. Kerr, 
leader of the propagation group of the Radiation 
Laboratory and was called specifically for the 
following purposes: 

1. To make those attending acquainted with each 
other and with the work then in progress. 

2. To review and summarize the general status of 
microwave propagation knowledge in the United 
States. 

3. To compare general measurement techniques. 

4. To standardize terminology and methods of 
presenting data. 

5. To formulate a program for future research and 
recommend any necessary redistribution of emphasis. 

The general conclusion reached by this conference 
was that the following subjects were of greatest 
importance: 

1. Perfection of the technique of radar range 
forecasting to a degree which would make it immedi¬ 
ately useful to the services, even if this had to be 
done in a preliminary form. 

2. Continuation of both theoretical and experi¬ 
mental investigation of the mechanism by which the 
properties of the atmosphere and earth affect micro- 



ORGANIZATION 


7 


wave propagation, under widely varying conditions 
of climate and terrain. 

3. Measurement of the reflection coefficients of 
land and sea surfaces over a wide range of angles of 
incidence, for the entire radar frequency spectrum, 
with a view to immediate application to radar 
coverage problems in the services. 

4. Establishment in the immediate future of an 
agency which could perform the following functions: 

a. Serve as a clearing house for all microwave 
propagat on information in the United States 
and organize future conferences of represen¬ 
tatives of agencies working in the propaga¬ 
tion field. 

b. Review the available knowledge from time 
to time and recommend any necessary redis¬ 
tributions of effort by investigating bodies. 

c. Act as responsible agency for the entire 
United States propagation investigation in 
dealing with groups working in similar fields 
in the United Kingdom and other Allied 
countries. 

Following this conference, Dr. I. I. Rabi, Head of 
the Research Division of the Massachusetts Institute 
of Technology Radiation Laboratory, suggested that 
Division 14 of NDRC take the initiative in setting 
up a microwave propagation committee to organize 
the more adequate program outlined ; n paragraph 4 
of the preliminary conference’s conclusions. During 
a subsequent consultation between Dr. Compton and 
Dr. Ralph Bown, Radio Research Director of the 
Bell Telephone Laboratories, Dr. Burrows was sug¬ 
gested as chairman of the proposed NDRC Commit¬ 
tee on Propagation. Dr. Burrows was chairman 
of the Radio Wave Propagation Committee of the 
Institute of Radio Engineers and had made numerous 
contributions to the knowledge of propagation. 

Under the NDRC Committee on Propagation a 
nation-wide program was proposed, to coordinate 
the work of such investigative bodies as the Radia¬ 
tion Laboratory, Bureau of Standards, Weather 
Bureau, various Army and Navy agencies, certain 
institutions cooperating with Division 13 of NDRC 
on direction finder problems, the Wave Propagation 
Committee of the Joint Communications Board 
[JCB], and such other bodies as the Committee on 
Propagation, after its official organization, might find 
helpful in furthering its program. 

On August 24, 1943, Dr. Burrows agreed to accept 
the chairmanship of the proposed Committee and at 
once began the work of organization and of surveying 


the activities of groups in the United States already 
engaged in propagation studies. 

The initial membership of the Committee as 
proposed by Dr. Burrows, after consultation with the 
men concerned and heads of the NDRC Divisions 
directly interested, was as follows: 

Dr. J. A. Stratton, Office of the Secretary of War. 

Dr. J. H. Dellinger, National Bureau of Stand¬ 
ards. (Chief of Section 13.2 and representing Divi¬ 
sion 13, NDRC.) 

Dr. H. H. Beverage, Radio Corporation of Amer¬ 
ica (representing Division 15, NDRC). 

D. E. Kerr, Radiation Laboratory, MIT (repre¬ 
senting Division 14, NDRC). 

A recommendation for these appointments was 
submitted to Dr. James B. Conant on October 5, 
1943. The Committee on Propagation was originally 
planned to be a part of Division 14, but shortly after 
its formation it was raised to the level of an NDRC 
committee, because the broadened scope of its direc¬ 
tive, as issued in November, clearly took in aspects 
of the propagation problem outside the field of 
Division 14 alone. Prior to this crystallization of the 
Committee personnel and while the group was in 
the formative stage and still under the jurisdiction 
of Division 14, Professor S. S. Attwood of the 
University of Michigan also served as a member. 
Later Prof. Attwood was detached from the Commit¬ 
tee to direct the Columbia University Division of 
War Research Wave Propagation Group [CUDWR- 
WPG], which was responsible under a contract to the 
Committee for the preparation of reports. This and 
other contracts are discussed in Chapter 2. 

During the closing months of 1944, Dr. Stratton 
resigned from membership. Shortly thereafter the 
membership was enlarged to include Dr. T. J. 
Carroll of the War Department and (somewhat later) 
M. Katzirr of the Naval Research Laboratory. 

During the first year the Committee operated 
without the services of a technical aide. Late in the 
summer of 1944, Dr. A. F. Murray and S. W. Thomas 
served temporarily in this capacity until a full-time 
aide could be obtained. This post was filled by R. J. 
Hearon from December 1944 until January 1946. 

The Committee retained the services of Dr. C. E. 
Buell, Chief Meteorologist of American Air Lines, 
who served as a consultant from March 15, 1944. 
Following completion of his work as director of the 
CUDWR-WPG, in October 1945, Prof. Attwood was 
made a consultant to the Committee. 




8 


ORIGIN AND ORGANIZATION 


13 LIAISON CHANNELS 

In general, liaison between the Committee and 
those organizations directly represented on it was 
through the individual concerned. Thus Dr. Dellinger 
provided liaison with Division 13, Mr. Kerr per¬ 
formed the same service for Division 14, and Dr. 
Beverage acted in this capacity for Division 15. 
Dr. Stratton served as liaison with the Office of the 
Secretary of War. 

In order to provide a similar close link with the 
Wave Propagation Committee of the Combined 
Communications Board [CCB], Dr. Burrows was 
appointed to membership on this Committee. 

In addition to these direct channels, a number of 
specialists from various Service organizations were 
appointed as liaison officers, in order to keep the 
work of the Committee closely coordinated with 
Service requirements and to speed the dissemination 
of information. 

Captain D. R. Hull acted in this capacity for the 
Navy, with R. S. Baldwin as alternate. Later Lt. 
Comdr. W. B. Chadwick was appointed as an addi¬ 


tional liaison officer for the Navy Department. 

Lieutenant Colonel J. J. Slattery served in this 
capacity for the Army, to supplement the liaison 
already provided through Dr. Stratton. 

Also, at the request of- the chairman of the 
Committee on Propagation, Comdr. F. W. Reichel- 
derfer, Chief of the Weather Bureau and Chairman 
of the Combined Meteorological Committee, assigned 
Lt. Col. H. Wexler to the Committee in the dual 
capacity of technical advisor on meteorology and as 
liaison officer for the CCB. 

Somewhat later Dr. Carroll and Comdr. D. H. 
Menzel were appointed to transmit propagation 
problems of the Army and Navy, respectively, to the 
Committee on Propagation under a directive of the 
JCB. 

In addition, use was made of established channels 
for contact with many agencies, including those in 
Allied countries. These channels included the Office 
of Scientific Research and Development Liaison 
Office, the Naval Coordinator of Research and 
Development, the War Department Liaison Officer, 
and the Office of Field Service. 



Chapter 2 

OBJECTIVES AND RESEARCH AGENCIES 


21 DIRECTIVE AND OBJECTIVES 

rr he original directive for the Committee on 

J- Propagation was issued by Dr. James B. Conant, 
NDRC Chairman, in November 1943 and read as 
follows: 

It shall be the duty of the Propagation Committee of the 
NDRC to organize and coordinate a program designed to 
secure the answers to problems on propagation of importance 
to the war effort. Its recommendations of contracts should be 
transmitted to the NDRC through Divisions 13, 14, and 15, 
and the supervision of the contracts remains with the Divisions 
which transmit the recommendations to the NDRC. It shall 
give consideration to the needs of Divisions 13, 14, and 15 
within the field in which it is limited. Information secured 
by this Committee and by corresponding sections of Divisions 
13, 14, and 15 shall be made mutually available as desired by 
the groups and may be used by the groups for the purpose of 
carrying out their missions. It is further understood that one 
of the duties of the Committee on Propagation is to assemble 
and analyze, and make available to appropriate agencies, all 
information in regard to propagation of importance to the 
wa r effort. 

The directive was purposely made broad enough 
to permit investigation in any direction promising 
useful results. In view of this breadth, it was neces¬ 
sary to establish a priority list of specific problems 
for immediate attack. Proper choice of the problems 
on this list was of great importance to the successful 
accomplishment of the Committee’s objectives and 
accordingly was taken up at the first regular meeting, 
held on October 13, 1943. During the course of this 
meeting the specific functions of the Committee were 
also defined, as follows: 

1. To coordinate the research then going forward 
in the United States and to initiate any new work 
necessary to round out the program. 

2. To review completely the existing data on 
propagation, correlate it, put it into a form usable 
in the Services, and disseminate it through author¬ 
ized liaison channels being set up for the purpose. 

3. To cooperate with similar agencies in the United 
Kingdom and other Allied nations for exchange of 
information and coordination of research, with a 
view to avoiding duplication of effort or of gaps in 
the investigation. 

With the establishment of these specific functions, 
two operational problems were selected as being of 
the highest priority. These were the tracking of 


storms and estimation of their properties with radar 
equipment and the prediction of range for all types 
of radio equipment employing that part of the 
electromagnetic spectrum above 30 me. 

The additional problems of determining necessary 
radar facilities, radar navigation along a shore line, 
and siting of direction finder equipment, were dis¬ 
cussed, but it was decided that these subjects were 
either outside the province of the Committee or were 
being adequately considered by other agencies. 

The following research problems were also agreed 
upon: 

1. Propagation in nonhomogeneous media. 

a. Meteorology. (1) A thorough review of avail¬ 
able instruments and methods for making 
atmospheric soundings and initiation of a 
program of manufacture of suitable types. 
(2) Development of techniques for employ¬ 
ing these instruments by means of sounding 
balloons, aircraft, etc. (3) Determination of 
the dielectric constant of the troposphere as 
a function of height, at locations within the 
United States or possessions where condi¬ 
tions in strategically important war theaters 
are reasonably well simulated. (4) Repetition 
of operations of (3) in selected strategically 
important regions or their meteorological 
equivalent, to obtain sample refractive index 
distributions. (5) Conduction of meteoro¬ 
logical weather analysis concurrently with 
functions under (3) and (4). (6) Sponsorship 
of further research into world-wide meteoro¬ 
logical conditions, their diurnal and seasonal 
variations, and their effect on propagation. 

b. Theoretical analysis of propagation. (1) Ex¬ 
tension of analytical methods to permit bet¬ 
ter physical understanding of the effects of 
varying refractive index distribution. (2) 
Preparation of working formulas for deter¬ 
mining field strength and fading charac¬ 
teristics. 

c. Establishment of experimental propagation 
measuring circuits in locations where results 
of (4) above make such experiments advis¬ 
able, these experiments to be correlated with 
simultaneous meteorological observation and 


9 


10 


OBJECTIVES AND RESEARCH AGENCIES 


weather analysis. Three frequencies were 
considered the minimum number capable of 
yielding a useful result. Those selected were 
24,000, 3,000, and 200 me, with 10,000 me 
considered as an alternate for 24,000, if 
equipment for the higher frequency was un¬ 
available. The characteristics of both one¬ 
way and two-way continuous wave and pulse 
transmissions were to be considered. 

d. Development of a technique for forecasting 
propagation conditions in the field, suitable 
for tactical and strategic use. 

e. Application of points mentioned above to 
specific operational problems in selected 
regions. 

2. Measurements of absorption of K-band radia¬ 
tion by atmospheric moisture in various forms and 
by dust or other scatterers. 

3. Study of the effects of the earth’s land and 
water surface on propagation. 

a. Determination of reflection coefficients of 
various surfaces for specular reflection and 
its effect on coverage of various radar and 
radio equipments. 

b. Study of back-scattering echoes from land 
and sea surfaces (ground clutter and sea 
return), with particular emphasis on effects 
at the highest frequencies to be employed. 

4. Investigation of storm echoes. 

5. Study of the shielding, diffraction, absorption, 
and depolarization effects of trees, hills, man-made 
structures, and other topographical features. 

6. Compilation, analysis, integration, and publi¬ 
cation of propagation information obtained, in forms 
suitable for use by the armed forces. 

This extensive program of investigation neces¬ 
sarily required agreement on an appropriate division 
of effort among United States, British, and other 
agencies available for the work. This division is 
discussed in the chronological record of the Com¬ 
mittee’s activities in Chapter 3. 

2.2 INVESTIGATING BODIES 

Very early in its existence the Committee con¬ 
sidered at length how best to implement the required 
research program. The conclusion was reached that 
making use of existing research agencies qualified to 
work in the propagation field, rather than setting 
up an independent research agency, would be most 


productive. This decision was influenced consider¬ 
ably by the serious shortages of personnel and equip¬ 
ment, and it was estimated that setting up a separate 
agency would have retarded progress of the investi¬ 
gation six months to one year. 

During the course of its investigations the Com¬ 
mittee maintained connections with a total of about 
66 separate agencies in the United States, Britain, 
Canada, New Zealand, and Australia, including the 
principal organizations within the armed forces of 
the Allied countries interested in propagation 
phenomena. 

Reports, recommendations, and requests from all 
these various agencies were received, analyzed, acted 
upon, and filed. This accumulated body of in¬ 
formation on propagational phenomena is listed in 
the Bibliography. These papers are referred to again 
in Chapter 4 under a summarization of the results 
of the Committee’s work. 

Of the agencies conducting actual theoretical or 
experimental research on radio wave propagation, the 
principal ones in the United States were as follows: 

1. Bell Telephone Laboratories [BTL]. 

2. Camp Evans Signal Laboratory. 

3. Columbia University Division of War Research 
[CUDWR]. 

a. Radiation Laboratory. 

b. Wive Propagation Group. 

4. National Bureau of Standards, Interservice 
Radio Propagation Laboratory, [IRPL]. 

5. Radiation Laboratory, Massachusetts Institute 
of Technology [MIT-RL]. 

6. U. S. Naval Research Laboratory. 

7. U. S. Navy Radio and Sound Laboratory. 

8. U. S. Army Signal Corps Operational Research 
Branch. 

9. Radio Corporation of America. 

10. Radio Research Laboratory, Harvard Uni¬ 
versity. 

11. U. S. Army Air Forces, Weather Division. 

There were also 2 agencies in Australia, about 21 

in Britain, 2 in Canada, and 2 in New Zealand. The 
number of agencies investigating propagation pheno¬ 
mena in the Allied countries totaled about 39. This 
relatively large number was necessitated by the 
importance, urgency, diversity, and complexity of 
the problem, and the physical difficulties of conduct¬ 
ing direct experimental investigation with usable 
accuracy under war, and at times under combat 
conditions. 

During the course of the Committee’s work, 



CONTRACTS AND PROJECTS 


11 


members visited the various investigating agencies 
to correlate the work when necessary, obtain first¬ 
hand information of the special aspects under investi¬ 
gation, or suggest a line of attack. Such visits are 
described in Chapter 3. 

2.3 CONTRACTS AND PROJECTS 

The entire organization and work of the Committee 
was carried on under the auspices of Army and Navy 
Project AN-16, pursuant to a recommendation of 
the Combined Meteorological Committee [CMC] of 
the Combined Chiefs of Staff, dated December 7, 
1943. This recommendation was made to the National 
Defense Research Committee in response to a request 
by the Combined Chiefs of Staff dated December 4, 
1943 and channeled jointly through the War Depart¬ 
ment Liaison Officer and the Coordinator of Research 
and Development. The Combined Chiefs of Staff 
asked specifically that: 

1. The Committee on Propagation of NDRC be 
requested to act as a coordinating agency for all 
meteorological information associated with short 
wave propagation. 

2. The Committee on Propagation be requested 
to forward periodically to the CMC a list of all 
reports and papers dealing with the meteorological 
aspects of short wave propagation which have been 
received or transmitted by that Committee. 

Originally contracts arranged with various agen¬ 
cies for research into propagation phenomena were 
handled through the contract machinery of the 
appropriate division of NDRC, specific recommen¬ 
dations for the terms of the contract being drawn 
up by the Committee. 

The NDRC later changed the manner of arranging 
contracts of the Committee on Propagation so that 
the Committee would recommend, and assume direct 
responsibility for, the contracts. At the same time 
the contracts that had already been let by Divisions 
13, 14, and 15 involving radio wave propagation 
were transferred to the Committee on Propagation. 
Such further extensions to these contracts as were 
required were arranged and recommended by the 
Committee on Propagation. 

Contract OEMsr-1207, let for the Committee, 
with Columbia University through the contract 
machinery of Division 14, was active from Novem¬ 
ber 1, 1943 to October 31, 1945. This contract was 
for collecting, analyzing, and integrating data on 


radio and radar wave propagation. Under its terms 
the CUDWR set up a Wave Propagation Group, 
directed by Professor S. S. Attwood, who had served 
on the Committee while that body was a part of 
Division 14. This group consisted of a scientific staff 
and stenographic and clerical personnel, and it 
handled the work described above, as well as periodic 
publication of reports for distribution according to 
a list approved by the NDRC chairman’s office. 

Contract OEMsr-728, with the State College of 
Washington, which was originally let through 
Division 14 and taken over by the Committee on 
Propagation after its formation, terminated on 
October 31, 1945. Work under this contract was 
under the direction of Dr. Paul A. Anderson of this 
college. The contract was a general one for the 
purpose of “carrying on experimental and analytical 
investigations in connection with the study of micro- 
wave propagation.” The first research conducted 
under its terms was a study of propagation along an 
overland path in the Pacific Northwest, where 
climatic and topographical conditions differed from 
those at San Diego and on the East Coast. 

Another project under this contract was the 
development of a portable low-level sounding instru¬ 
ment for measuring temperature and humidity gradi¬ 
ents in the lower atmosphere. Subsequently this 
apparatus was adopted by the U. S. Navy and several 
other United Nations military and scientific agencies. 

Production of an improved model of this equip¬ 
ment was also carried out, with subsequent deliveries 
to the Army Air Forces [AAF], the Naval Research 
Laboratory [NRL], the Department of Scientific and 
Industrial Research in New Zealand, and to Dr. Paul 
C. T. Kwei and Dr. Eugene T. Hsu for use in China. 

Performance of the sounding apparatus under 
tropical conditions and tests to determine the feasi¬ 
bility of predicting nonstandard radar coverage by 
means of atmospheric soundings were the objects of 
another project, which was carried out in Panama in 
collaboration with the NRL. 

Another very important project under this contract 
was Office of Field Service Project SWP-3 which was 
for the purpose of exploring meteorological condi¬ 
tions in the Southwest Pacific theater to determine 
their effects on radar coverage, and to assist the AAF 
in establishing a forecasting service for the tactical 
exploitation of nonstandard propagation in that 
region. 

A member of the State College of Washington 
group working under this contract was loaned to 




12 


OBJECTIVES AND RESEARCH AGENCIES 


the NRL staff to assist in an experiment at Antigua 
early in 1945. This experiment investigated and 
established the existence of surface air layers having 
significant effects on radar coverage over large areas 
of the ocean. 

Contract OEMsr-1502 between the Committee 
and the Jam Handy Organization of Detroit was in 
force from May 7, 1945 to December 31, 1945. The 
contractor undertook the production of a motion 
picture and various other training aids, designed 
primarily for use by the armed forces in educating 
personnel concerned with propagation phenomena, 
and secondarily to acquaint all agencies concerned 
with progress made. 

Contract OEMsr-1496 between the Committee 
and the University of Texas was in force from June 1, 
1945 to October 31, 1945. This contract required the 
contractor to develop equipment for, and make 
measurements of, deviations in angle-of-arrival of 
microwaves propagated through the lower atmos¬ 
phere. It was designed also to supplement and expand 
knowledge of the deviations in angle-of-arrival 
already obtained through experiments conducted by 
the BTL. These deviations were considered large 
enough to affect the accuracy of gunlaying radars 
and similar equipments. 

Contract OEMsr-1497 with the Humble Oil 
Company of Texas was in force from June 2, 1945 
to October 31, 1945. Under its terms the contractor 
undertook construction of certain field strength 
measuring equipments for use in experiments being 
carried on as part of Project AN-16 in the Naval 


Research Laboratory, Navy Radio and Sound 
Laboratory, and the Army’s Camp Coles, Camp 
Evans, and Watson Laboratories, and by the New 
Zealand Joint Communications Board. 

These five contracts make up the total of direct 
contractual relationships entered into by or on behalf 
of the Committee on Propagation but represent only 
a small portion of the work on propagation problems 
carried on in the United States. The bulk of actual 
research was conducted under contracts let by 
Divisions 13, 14, and 15 and by the Service in 
conjunction with laboratories and industrial com¬ 
panies. The Committee served as the integrating, 
analyzing, and disseminating body for the results 
of all such work bearing on the propagation problem. 

In addition to carrying on the general integration 
of reports and papers from all sources (see list of 
sources in the Bibliography), the Committee spon¬ 
sored three conferences which were attended by 
representatives of most of the agencies investigating 
propagation phenomena. A similar conference was 
held before the Committee was in being, and a report 
of the proceedings was published by the Wave 
Propagation Group of the MIT Radiation Labora¬ 
tory. The fourth and last conference on propagation, 
the third held under sponsorship of the Committee, 
was attended by 236 persons, representing approxi¬ 
mately 59 separate agencies in and out of the armed 
forces of the Allied nations. This meeting took place 
May 7, 8, and 9, 1945 in Washington, D. C. Full 
reports of this and previous conferences are listed 
in the Bibliography. 



Chapter 3 

CHRONOLOGICAL RECORD 


3i COMMITTEE ACTIVITIES 

T he Committee on Propagation was organized 
in Division 14 of the National Defense Research 
Committee, in response to an urgent request by Sir 
Edward Appleton, Director of the Department of 
Scientific and Industrial Research of Great Britain. 
This request was specifically for United States 
cooperation in a more adequate investigation of radio 
wave propagation. Observed variations of radar 
coverage and performance over a considerable range 
of climatic and meteorological conditions had already 
revealed the need for a thorough understanding of 
the influences of such conditions on radio wave 
propagation, particularly at frequencies above 30 me. 
Also, the effects of back scattering of radiation from 
the sea surface (sea return) under various wind and 
wave conditions and of land surface topographies of 
various types on radio wave propagation, particu¬ 
larly at angles approaching the horizontal, were 
already known to be serious. These and similar 
factors had been established by reports from opera¬ 
tional installations as having profound significance 
in the operational employment of radio devices, and 
the fundamental mechanisms producing these effects 
were not well understood. 

A preliminary conference on propagation was held 
at the Massachusetts Institute of Technology [MIT] 
Radiation Laboratory [RL], July 1 and 2, 1943. A 
report of this conference was published by the 
Laboratory. It contained a statement of the general 
program of investigation held desirable and recom¬ 
mendations for setting up a body to coordinate the 
activities of research agencies with needs of the 
armed forces and with work on the problem already 
in progress in Allied countries. This body, which 
became known as the Committee on Propagation, 
was organized as explained in Chapter 2, with 
Dr. Chas. R. Burrows as chairman. 

Dr. Burrows accepted "the chairmanship on August 
24, 1943, proceeded immediately with organization 
of the full Committee, and began the task of estab¬ 
lishing and correlating a program of research. 

Dr. Burrows and Donald E. Kerr, head of the 
Wave Propagation Group at the Radiation Labora¬ 
tory and a member of the Committee on Propaga¬ 


tion, conferred in Washington on September 2 with 
Dr. A. F. Murray of NDRC and with Doctors H. 
Hopkins and W. Ross of the British Central Scientific 
Office. A complete set of reports of British work on 
propagation was available in this office, and this 
was placed at the disposal of Dr. Burrows and the 
Committee. The desirability of extending the investi¬ 
gation down to 27 me was discussed in connection 
with improving the efficiency of certain equipments 
using those frequencies. 

On September 3, Dr. Burrows and D. E. Kerr con¬ 
ferred with Dr. J. A. Stratton in the Office of the 
Secretary of War regarding Dr. Stratton’s serving on 
the Committee and the possibility of minimizing or 
eliminating ground return in radar operation at low 
angles. Comdr. F. W. Reichelderfer, head of the 
Weather Bureau, was also contacted, and the use of 
radar in locating storm areas was taken up. 

During the remainder of September the organiza¬ 
tion of the Committee was pushed forward, with 
the result that the names of Stratton, Dellinger, 
Beverage, and Kerr were formally proposed for 
membership to the Office of the Chairman, NDRC. 

The first official meeting of the Committee on 
Propagation was held on October 13, 1943, with the 
following members and representatives of interested 
agencies: Dr. Chas. R. Burrows, Chairman; Dr. J. 
H. Dellinger, Division 13, NDRC; D. E. Kerr, 
Division 14, NDRC; Dr. H. H. Beverage, Division 
15, NDRC; Dr. J. A. Stratton, War Department; 
J. H. Teeter, representing the Chairman, NDRC; 
Dr. H. G. Hopkins, representing the British Central 
Scientific Office; and Lt. (jg) J. M. Bridger, repre¬ 
senting Captain D. R. Hull of the Navy Depart¬ 
ment. 

The field of propagation was reviewed, the specific 
functions of the Committee were defined, and a list 
of definite problems for both immediate and longer 
term consideration was drawn up. It was agreed 
that the Committee would confine itself to the study 
of tropospheric propagation, at least at first, with 
special emphasis on problems of nonstandard 
propagation. 

On October 15 Professor S. S. Attwood of the Uni¬ 
versity of Michigan agreed to assist Dr. Burrows in 
directing the activities of the Committee. Later 


13 


14 


CHRONOLOGICAL RECORD 


Prof. Attwood was appointed Director of the Colum¬ 
bia University Wave Propagation Group [CUDWR 
WPG] which operated under contract OEMsr-1207, 
to integrate, analyze, and disseminate reports of 
research. This contract went into force on Novem¬ 
ber 1, 1943. 

Dr. Burrows, Prof. Attwood, and D. E. Kerr flew to 
England November 22, 1943, to confer with British 
investigators and secure integration of the United 
States and British programs. As a result of this visit, 
a unified program of research was agreed upon, with 
certain divisions of effort to prevent duplication of 
particular phases of the work, and to insure covering 
all practical aspects of the problem. The British 
agreed to continue experiments on wavelengths of 
9, 6, and 3 cm, with parallel measurements of 
meteorological factors, and also to undertake 
measurements at 1.25 cm when equipment became 
available. The effects of hills and trees on the shorter 
wavelengths was also to be studied. They were also 
to continue theoretical investigations already under 
way with special emphasis on use of the Manchester 
University differential analyzer. 

It was agreed that American agencies would make 
detailed measurements to determine the character¬ 
istics of water vapor diffusion in a warm air mass 
blowing over cold water, with accompanying radio 
transmission tests at wavelengths of roughly 10 and 
50 cm. A team of research workers was to be organ¬ 
ized and equipped to make simultaneous propagation 
and meteorological measurements at locations pro¬ 
viding conditions similar to those encountered by 
radar-using personnel of the armed forces. Tests on 
1.25-cm waves were to be made along the eastern 
coast of the United States as apparatus permitted, 
to provide data on propagation conditions typical 
of the eastern coast of a large continent. 

It was agreed also that Dr. John E. Freehafer of 
MIT-RL would be sent to Britain in order to obtain 
closer cooperation in theoretical attacks being made 
on these problems. 

It was further agreed to make a study of atmos¬ 
pheric absorption, particularly at 3-cm and shorter 
wavelengths, and of absorption by rain, fog, dust, 
and other such phenomena. The reflection coefficient 
of the sea for radiation of 10-cm and possibly 3-cm 
and shorter wavelengths was to be studied for graz¬ 
ing angles less than 5 degrees, and the back-scatter¬ 
ing effect was also to be investigated. Storm echoes 
and their possible tactical uses were also to be 
treated. In addition, the United States was to set up 


and maintain a group to compile, analyze, integrate, 
and disseminate propagation information. 

It was jointly agreed to interchange samples of 
meteorological instruments most useful for measure¬ 
ments in connection with propagation studies. 

Upon return to the United States of this mission, 
in January 1944, offices were occupied in the Empire 
State Building, New York City, jointly with the 
Wave Propagation Group of Columbia University 
Division of W ir Research. 

On February 12, 1944, a meeting was held at 
which liaison representatives from the armed forces 
presented certain urgent Service requirements and 
outlined experimental programs that the respective 
branches were prepared to undertake in cooperation 
with the Committee. 

One of the most urgent needs in the Services was 
for a handbook and other instructional aids, prepared 
in the simplest practicable form for the use of opera¬ 
tional personnel with limited technical background. 
It was proposed that the Columbia University Wave 
Propagation Group, which had been set up in accord 
with the program agreed on with the British, should 
undertake the preparation of such aids to instruction. 

At a meeting held February 15, 1944, a statement 
outlining the propagation problem was drawn up, 
with proposals for Service cooperation in experiments 
devised to provide solutions to the most urgent 
aspects of the question. This statement set forth the 
NDRC Committee’s view that the problem of “non- 
ionospheric propagation in a nonstandard atmos¬ 
phere” should be given highest priority, and it gave 
details of experiments proposed or already under 
way. Five specific experiments were outlined, in each 
of which the assistance of the Services was required. 
These were as follows: 

1. Organization and equipment of a complete 
transportable field unit for conducting propagation 
experiments, which could be sent to any region 
considered likely to yield results useful in the opera¬ 
tional theaters. This experiment would require con¬ 
siderable apparatus and a team of trained research, 
operational, and maintenance personnel. Dr. Paul 
Anderson of the State College of Washington 
provided a considerable amount of material on this 
project. 

2. An over-water experiment along a path between 
Cape Ann and Cape Cod was to be carried out by 
MIT-RL, to obtain information on propagation 
characteristics along the eastern coast of a continent. 
These data would be applicable to similar regions in 



COMMITTEE ACTIVITIES 


15 


war theaters, particularly near the Chinese north¬ 
east coast. 

3. A detailed experiment was considered desirable 
in a region where stable temperature inversions were 
produced in the atmosphere by subsidence of upper 
layers of air. Such experiments were already being 
conducted by the U. S. Navy Radio and Sound 
Laboratory [NRSL] along several over-water paths 
near San Diego, California. 

4. An experiment near the Panama Canal Zone 
was planned by the Navy in cooperation with the 
State College of Washington group under Anderson, 
to establish a correlation between meteorological 
conditions of that region and radar performance. It 
was expected that this would provide a good test of 
equipment and methods under tropical conditions 
and that the information obtained would apply in 
other similar regions. 

5. An experiment was proposed to be conducted 

in Florida, with the aid of Signal Corps and Air 
Force personnel utilizing equipment already in the 
area. It was expected that this project would yield 
considerable information on means of predicting 
propagation characteristics for localities climatically 
similar. , 

Meantime the Columbia University Division of 
War Research Wave Propagation Group [CUDWR 
WPG], directed by Prof. Attwood and operating 
under contract OEMsr-1207, was preparing a report 
on tropospheric propagation for radar operators, offic¬ 
ers, and other operating personnel, at the request of 
the Combined Communications Board [CCB] and 
Combined Meteorological Committee [CMC]. This re¬ 
port, compiled from all established data on variations 
in radar coverage available, was prepared in as non¬ 
technical and popular a style as possible. It received 
the approval of the Wave Propagation Committee 
of the CCB, and about 30,000 copies were distributed 
to the armed forces of the United Nations during 
June 1944 under the title Variations in Radar Cover¬ 
age (JANP-101). This report helped to clarify the 
problem of nonstandard propagation for Service 
personnel and to throw light on certain peculiarities 
in radar performance and coverage variations caused 
by newly discovered meteorological conditions (see 
Chapter 16). During early 1944, a bibliography of 
publications on propagation was prepared and 
published by the CUDWR WPG. 

At a meeting on February 28, 1944, a direct request 
from General MacArthur to NDRC was laid before 
the Committee, which asked that a group of scien¬ 


tists be sent to Australia to study radar and commu¬ 
nication problems in that area of the Pacific theater. 
It was finally arranged that the communication part 
of this request would be handled by the Signal 
Corps and that the radar portion would be fitted 
into the general research program already in process 
of organization. 

Out of the series of meetings and conferences held 
during February, a program of four principal points 
was developed which was presented on March 4, 
1944, to the Wave Propagation Committee of the 
Joint Communications Board. This program was 
accepted and put into effect soon afterward, as 
follows. 

1. A working group under the direction of Dr. 
Anderson proceeded to the Canal Zone to conduct 
meteorological measurements in cooperation with 
the Navy. Following completion of this work, the 
group proceeded to Australia and performed similar 
investigations as requested by General MacArthur. 
This work was carried on under contract OEMsr-728, 
with the State College of W ishington. Arrangements 
were also made for training a group of about 20 
Army and Navy officers in use of the meteorological 
measurement technique and apparatus developed by 
Dr. Anderson. These officers were later to be sent into 
the field to organize teams for making meteorological 
soundings. 

2 . The Wave Propagation Group of the MIT-RL 
under D. E. Kerr conducted a study along an over¬ 
water path on the east coast of the United States, 
as outlined previously. 

3. The NRSL investigation of propagation under 
subsidence conditions was continued. 

4. Propagation conditions over land were planned 
for study by Canadian Army research groups. Pre¬ 
liminary discussions were held with these groups 
early in 1944. 

On March 13, Dr. Burrows and Prof. Attwood con¬ 
ferred with the staff of the NRSL in San Diego in 
connection with the investigation of propagation 
under subsidence conditions. The research was in¬ 
tegrated into the general program and reported to the 
Joint Communications Board [JCB] on March 29. 

As a result of this visit the NRSL agreed to modify 
and expand its propagation research extensively to 
include tests over a number of different paths, using 
both one-way and radar transmissions, with simul¬ 
taneous meteorological measurements. These experi¬ 
ments were to be measurements of propagation on 
three representative frequencies along a 108-mile 



16 


CHRONOLOGICAL RECORD 


over-water path between Los Angeles and San Diego, 
and comparable frequencies between San Diego and 
San Pedro, a distance of 80 miles over water, using 
suitable antenna heights. Atmospheric soundings 
were to be taken from a ship at a point midway along 
such paths and also on shore as near the midpoint 
as possible. Measurements with a blimp to determine 
the extent of uniformity of the inversion layer were 
also projected. 

Measurements were to continue on fixed radar 
targets located at various altitudes and along various 
azimuthal bearings. Field strength measurements 
were also to be made from an aircraft flown at sig¬ 
nificant altitudes over the transmission paths, the 
results to be correlated with meteorological data. 
The chairman assisted inauguration of this expanded 
program by using the Committee’s powers and in¬ 
fluence in obtaining additional apparatus required. 
In addition, information was exchanged with mem¬ 
bers of a British scientific delegation who were 
present, and considerable effort was directed to ob¬ 
taining a meteorologist for full-time work with the 
NRSL group conducting the experiment. 

On April 3, Dr. Burrows, Comdr. J. L. Reinartz, 
and Lt. Comdr. D. H. Menzel visited Panama to 
observe the experiments being conducted jointly by 
Dr. Anderson’s group and the Navy. 

As a result of this visit, substantially better and 
more extensive cooperation between the scientific 
group and Service forces in the area was obtained, 
and an analysis of the data obtained to date was 
secured, which revealed occurrence of a predictable 
surface duct condition. 

A conference was held in Washington on May 2, 
1944, at which representatives of the various research 
agencies of the United States interested in propaga¬ 
tion were present. A large amount of propagation 
information was exchanged by presentation of many 
papers describing various experimental and theo¬ 
retical researches going on in various countries. The 
complete record of papers and proceedings was 
published by the CUDWR WPG and is contained in 
the Bibliography at the end of this volume. 

Special consideration was given to the question of 
symbols and nomenclature by a committee headed 
by Prof. Attwood. A list of such symbols was pre¬ 
pared by this committee and was accepted without 
dissent by the Wave Propagation Committee of the 
CCB on May 17, 1944. 

On May 23 the chairman of the Committee on 
Propagation presented to the NDRC a report on 


what had been accomplished up to that time by the 
Committee and its plans for the ensuing year, to¬ 
gether with budget requirements. The budget was 
approved with minor deletions in the items covering 
contingencies. 

On June 29, 1944, a meeting was held at which the 
progress of the various experimental projects was 
reviewed in some detail. Two Armed Service requests 
were also taken up. The first, submitted by Comdr. 
Menzel and Dr. T. J. Carroll, dated June 12, 1944, 
outlined the general needs of the Services. Copies of 
this letter were forwarded to the Committee members 
for their consideration before the meeting convened. 
The second was received from General Colton, in 
the Office of the Chief Signal Officer, and specifically 
requested a theoretical investigation of the effects of 
low-level tropospheric layers on propagation at wave¬ 
lengths near 10 and 3 cm. 

After discussing specific requirements of the services 
as laid down in the Menzel-Carroll letter, certain of 
the questions were referred to appropriate agencies 
for solution. In particular, MIT-RL undertook to 
study the effects of refraction on gunfire control 
radars operating in the 10- and 3-cm bands. Most of 
the other questions raised were already under inves¬ 
tigation but were not yet sufficiently advanced to 
permit of conclusive answers. General Colton’s re¬ 
quest was considered to be covered by the action 
taken in connection with the Menzel-Carroll letter. 

In addition to progress reports from United States 
research agencies, a report on British work was sub¬ 
mitted, particularly on the status of 9-6-3-cm experi¬ 
ments over the Irish Sea. Little useful correlation 
between propagation and meteorological factors had 
yet been obtained in this experiment. Projected 
British experiments included investigation of absorp¬ 
tion and attenuation of 10- and 3-cm band radiation 
in oxygen, in water in all forms occurring in the 
atmosphere, and in salt spray. 

Late in June 1944, the need for closer liaison 
between the Committee and CMC was met by the 
appointment of Major H. Wexler of the Army Air 
Forces, Weather Division, as a technical advisor. 
This also strengthened the meteorological represen¬ 
tation associated with the Committee, which had 
not formerly been completely adequate. 

The Committee met at the Radiation Laboratory 
on August 4, 1944. During this meeting plans were 
laid for an extensive conference on propagation to 
be held in Washington, D. C., on November 16 and 
17, at which representatives of research agencies in 



COMMITTEE ACTIVITIES 


17 


all the countries engaging in propagation research 
could present findings to date. 

Plans were laid for Dr. Anderson’s trip to the 
Southwest Pacific theater in response to General 
MacArthur’s request for investigation of propagation 
phenomena. This project was of considerable im¬ 
portance and is more fully described elsewhere in 
this report. 

A report by Dr. Svein Rosseland, assistant to Prof. 
Attwood in the CUDWR WPG, was heard, on work 
going on in England and on data brought back to 
that country by Dr. Booker. These data described 
radar echoes from points more than 1,500 miles 
from the 200-mc Bombay, India, station, which had 
been observed during the season following the 
northeast monsoon. 

Other reports were heard on Bell Telephone 
Laboratories [BTL] experiments on K band along 
a path to Atlantic Highlands and similar experiments 
by MIT-RL near Boston. No nonstandard propaga¬ 
tion had been observed at Atlantic Highlands,.but 
some had occurred in the Boston area. 

Experiments of MIT-RL along a ten mile path 
had indicated the impossibility of measuring the 
effect of oxygen and water vapor outside the labora¬ 
tory itself. 

Dr. W. H. Furry described the work of preparing 
coverage diagrams for radar and VHF (very high 
frequency) communication equipment under ground- 
based duct conditions. Owing to the volume of 
calculations required in this work it was decided to 
obtain use of the Harvard University automatic 
sequence-controlled calculating machine, which 
would effect a probable reduction in the time required 
from an estimated nine or ten months to about three 
weeks. This proposal was subsequently carried out. 

Dr. Beverage presented certain problems of Divi¬ 
sion 13, particularly the need for supplying the best 
information on probable coverage to signal officers 
in the field at the earliest possible date. Estimates 
based on the V> earth radius formula tended to be 
pessimistic. 

Dr. H. Goldstein presented information on the 
problem of fluctuating signals. Instability in the 
equipment was a source of great difficulty, but, when 
this had been overcome, such results as were obtained 
indicated that most fluctuation was due to inter¬ 
ference. 

Plans were made for a field trip to observe the 
extensive MIT-RL experiments proceeding on four 
different wave bands along a path between Race 


Point and Gloucester. On this trip the entire ap¬ 
paratus and organization of the experiment were 
inspected and discussed. 

A detailed memorandum of the Committee’s 
current work was submitted on August 10 to the 
Chiefs of NDRC Divisions 13, 14, and 15, in order 
to keep these groups informed of developments. The 
breakdown of activities described five well-controlled 
experiments which were under way in different 
meteorological environments and the theoretical 
attack proceeding in Britain and the United States. 
These experimental attacks on the problem have 
been described earlier in outlining the Committee’s 
program for the year. The memorandum referred to 
here specifically invited Division comment on the 
program in progress and requests for other investi¬ 
gations if additional ones seemed desirable. 

A Committee meeting on September 21, 1944 
considered new humidity measuring instruments and 
reviewed progress of the work under way at RL. 
This was reported by D. E. Kerr as nearing the conclu¬ 
sion of the experimental work. The matter of educa¬ 
tional films to disseminate propagation information 
to the Services was brought up, and the need for a 
technical aide to the Committee who should be 
familiar with NDRC procedure was discussed. Dr. 
Burrows stated that efforts were being made to 
obtain a contractor who would make meteorological 
measurements along the BTL to Mt. Neshanic prop¬ 
agation path, for correlation with the transmission 
data available at BTL. These measurements were 
later undertaken by the Airborne Instruments Lab¬ 
oratory [AIL] of Mineola, Long Island. The matter 
of eventual demobilization of OSRD was discussed, 
particularly as to effects of such demobilization on 
investigations of propagation then in progress. 

The Committee met again on November 15, 1944 
to consider replies received from Divisions 13, 14, 
and 15 to the memorandum outlining its program in 
progress submitted on August 10 and to transact 
other business. The matters of calculation of radar 
coverage diagrams for nonstandard conditions, of 
the range and reliability of very high frequency 
[VHF] and ultra high frequency [UHF] communica¬ 
tions links, and the choice of frequencies for such 
links were taken up in detail. After thorough con¬ 
sideration, a reply was drafted for the Divisions 
concerned, particularly Division 13, stating that 
available information on propagation did not permit 
preparation of accurate coverage diagrams for such 
communications circuits on any other basis than 



18 


CHRONOLOGICAL RECORD 


that of 14 earth radius, as was already being done. 
It was expected that work then in progress would 
modify the limitation as it progressed. In the matter 
of choice of VHF, UHF, and super high frequencies 
[SHF], information was not yet available, but surveys 
under way were expected to provide some back¬ 
ground, although the intricacy of the problem did 
not encourage hope of an early complete solu¬ 
tion. 

The difficulties involved in the preparation of field 
strength contours appeared so formidable that 
requests from the Services for preparation of such 
contours was withdrawn, and a new request was 
substituted. This asked that workers on theoretical 
or observational and experimental programs forward 
as informal memoranda such examples of correlations 
between meteorological conditions and propagation 
characteristics as could be applied directly in the 
field, with suggestions for possible tactical applica¬ 
tions. This substitute request was received by the 
Committee in November. 

In addition, an important report by Dr. Anderson 
from the Southwest Pacific theater was considered 
which described the progress of project PDRC-647 
which members of the State College of Washington 
staff had undertaken under Contract OEMsr-728. 
Its objectives were to explore meteorological condi¬ 
tions in the Southwest Pacific theater to determine 
their effects on propagation, and to assist the Army 
in establishing a forecasting service for the tactical 
exploitation of nonstandard propagation in that 
region. 

After several conferences between Dr. Anderson’s 
group, various Australian agencies, and representa¬ 
tives of the Air Signal Office, Far East Air Force 
[FEAF], headquarters for the mission was established 
at the Radio Physics Laboratory at Sydney. Meet¬ 
ings were held here with Professor F. W. G. White 
and representatives of the Royal Australian Air 
Force and Royal Australian Navy. The following 
facts were brought out. The Australian and NDRC 
programs supplemented each other without duplica¬ 
tion of effort, making revision of plans unnecessary. 
An acute need existed for definite information con¬ 
cerning low-level meteorological conditions in the 
oceanic areas of the Southwest and Central Pacific. 
This information could best be obtained by NDRC 
and United States Army groups. 

Rough forecasting of nonstandard propagation 
along the southeast, south and southwest coasts of 
Australia was possible, correlating superrefraction 


data collected from radar stations with synoptic 
meteorological data. 

Observations from North Australia showed no 
similar clearcut correlations. Reports from New 
Guinea and the Solomon Islands were too meager 
to be useful. 

A Radio Physics Laboratory [RPL] experimental 
program was projected at a location near Darwin, 
Australia, which would be correlated with land, ship- 
based, and aircraft soundings and synoptic weather. 
A low-level sounding equipment was delivered to 
RPL for use in these experiments. 

A conference was held at the Radio Development 
Laboratory in New Zealand at which a low-level 
sounding equipment was delivered and trial sound¬ 
ings taken by Dr. Anderson. As a result of this meet¬ 
ing, a long-range program was agreed on in addition 
to the work already being conducted by New Zea¬ 
land agencies. This program would take advantage of 
the unusual conditions offered by the persistent 
Fohn winds which override the cold water at the 
eastern coast. 

Dr. Stephenson of Dr. Anderson’s group began the 
collection of meteorological and oceanographic data 
available in Australia preliminary to the selection 
of optimum sites for radar-weather observations. 
New information was available on continental and 
general equatorial meteorology but very little for 
the ocean area to the west and north of New Guinea. 

Recommendations for establishment of a limited 
number of radar-weather stations in the Biak-Owi- 
Noemfoor region were submitted to the FEAF late 
in August. These recommendations were approved 
after some discussion, but the plans were changed 
when FEAF headquarters suggested the usefulness 
of an Army radar-weather team with sounding 
equipment in the projected operations at Leyte. 
Preparations were made to take advantage of this 
suggestion. 

Consideration was given to determination of the 
low-level conditions characteristic of the Southwest 
and Central Pacific oceanic areas, with tentative 
conclusions from data secured during the summer 
of 1944 that strong ducts to 40 or 50 ft and weaker 
stratifications to 800 or 1,000 ft were common in 
the region, especially in late afternoon. In the dol- 
drum region standard conditions were the rule. The 
need for more complete measurements was pointed 
out, and the use of PT boats and seaplanes to 
obtain them was secured. 

Approval for measurements in the region near 



COMMITTEE ACTIVITIES 


19 


Saipan was also obtained, and arrangements were 
begun for the transfer of personnel to that theater. 

Further informal conferences were held with 
Australian and British groups, from which these 
conclusions were drawn. General meteorological data 
did not provide sufficient information quickly to be 
of practical use in forecasting propagation in a .given 
area. Instead, intensive ground-based and aircraft 
soundings offer the most practical means for setting 
up a short-range forecasting service for radar and 
radio communication coverage. 

At a formal conference with the same groups a 
policy to be adopted by the Australian Services was 
decided upon. An operational program similar to the 
NDRC Office of Field Service program was outlined 
by the members and approved for immediate inau¬ 
guration. A radar-weather school was to be set up 
in the Meteorological Section of the RAAF for 
training radar-weather officers. Arrangements for 
manufacturing sounding equipment were also made, 
with almost all components planned for production 
in Australia. 

Plans for expanding the operational program at 
Leyte were laid, and arrangements for observations 
at Saipan were also concluded. Measurements at 
Woendi Island were planned to continue until definite 
results were obtained, and arrangements were also 
made for transferring direction of the project to an 
officer of the Fifteenth Weather Region Headquar¬ 
ters, after which all civilian personnel with the 
exception of Mr. Grover would return to the United 
States. Mr. Grover would remain for the purpose of 
maintaining contact between the U. S. Army, 
Australian, and NDRC programs. 

Finally, recommendations for future procedure in 
this theater were made, which included maintaining 
at least one civilian research meteorologist in the 
area, and perhaps a group with the Army in China. 

Another conference on propagation was held during 
November 1944, attended by representatives of the 
investigating laboratories and armed forces of the 
Allied Nations. A large number of papers were 
delivered on propagation and related subjects. A 
full report of this conference was prepared by the 
CUDWR WPG and distributed to approved agencies. 

At the next meeting of the Committee, held on 
December 9,1944, a number of new matters were taken 
up, as well as the status of work already in progress. 

A group of British research workers, who had been 
conferring with United States propagation workers 
during a tour of laboratories in this country, reported 


on their findings. Dr. Booker also gave a detailed 
account of the work going on in Australia, as seen by 
him during a visit to that country which he had just 
concluded. The joint United States-British program 
was discussed, as well as methods of interpreting 
results of propagation experiments, calculations of 
coverage diagrams, and the proper dissemination of 
a report, Tropospheric Propagation and Radio Meteor¬ 
ology, which had been prepared by CUDWR WPG. 
This report, distributed in December, was a compact 
but thorough summary of the established informa¬ 
tion on propagation obtained to the date of its prep¬ 
aration. It was on a practical but much more quan¬ 
titative level than Variations in Radar Coverage 
issued earlier under auspices of JCB. It proved to be 
of considerable value to radar officers, particularly in 
improving the confidence and efficiency of radar 
operating and siting personnel, who had previously 
had at best only qualitative conceptions of such ef¬ 
fects as superrefraction and trapping of radiation 
in ducts. 

A subcommittee of the Committee on Propagation 
met on December 30, 1944, and heard a personal re¬ 
port by Dr. Anderson on his mission to the Southwest 
Pacific during the middle of the year just ending. 
From the results of this mission it was apparent that 
low-level ducts existed over substantial areas of the 
ocean in the trade wind regions which had profound 
effects on propagation characteristics of radar and 
VHF radio frequencies. These propagation charac¬ 
teristics were also found to vary markedly with 
heights of transmitting and receiving antennas. After 
consideration of these findings, the subcommittee 
decided that a carefully controlled experiment under 
similar conditions was an urgent necessity, in order 
to reduce these qualitative indications to reasonably 
accurate quantitative data, which could be applied 
by operational personnel in theaters where similar 
conditions existed. It was decided that an experi¬ 
ment conducted directly by the Navy at a suitable 
location in the Caribbean area would be most prac¬ 
ticable, and plans were drawn up for a detailed 
investigation by one-way and radar transmission on 
several frequencies. 

In response to a request from Brigadier General 
Borden the Committee arranged on December 14 
for establishment of a meteorological sounding station 
in the Southwest Pacific [SWP] area. On December 
19 a letter was drafted and despatched to Dr. E. M. 
Marsden, Director of Scientific Developments in the 
Department of Scientific and Industrial Research in 





20 


CHRONOLOGICAL RECORD 


New Zealand. This letter commented on the work 
already accomplished, as reported to the Committee 
by Dr. Anderson and Dr. Booker, and invited expan¬ 
sion of the investigation, particularly to determine 
the effects on propagation of a hot, dry, air mass mov¬ 
ing from the land out over the sea. This condition 
existed in many other operationally important 
regions of the Western Pacific and was known to 
affect seriously the performance of coastal radar 
installations. 

On January 1, 1945, Dr. Stratton asked to be re¬ 
lieved of his responsibilities as a Committee member 
and accepted in lieu thereof an appointment as a 
consultant, which capacity permitted him more time 
for discharging his duties in the Office of the Sec¬ 
retary of War. 

At a meeting held on January 5 many questions 
were taken up, and progress made in the preceding 
year was reviewed. 

The following projects were reported as proceeding 
concurrently. 

1 . The Navy experiment along an over-water path 
in the Caribbean area, where thin surface ducts were 
prevalent. 

2. Experiments where relatively dry air moved 
from the land over a water surface. These included 
the MIT-RL experiment near Cape Cod and analysis 
of the data obtained, and experiments going on in 
New Zealand. 

3. Propagation over a land surface where radiation 
cooling produced temperature inversions in the lower 
air layers. An experiment was being conducted in 
Arizona by NRSL, and another was being prepared 
in Canada by the Army Operational Research 
Group. 

4. Experiments along an over-water path where 
subsidence of an upper air mass produces duct condi¬ 
tions. The NRSL was conducting such experiments 
near San Diego, which offered conditions typical of 
certain other areas in the Pacific. 

5. Developments of meteorological theory for low- 
level ducts in purely oceanic air. This work was 
going on at MIT-RL. 

6 . Development of atmospheric sounding equip¬ 
ment for the armed forces. This work was going on 
at the State College of Washington. 

7. An educational program designed to provide 
the Services with up-to-date information on the 
propagation question. This was being carried out 
by Columbia University. 

8 . Mathematical calculations of wave propagation 


characteristics. These calculations were being con¬ 
ducted by CUDWR WPG and by MIT-RL. 

In addition, certain new questions were taken 
up with a view to arranging experiments to provide 
the answers. These were the matters of accuracy of 
gun-laying radars as affected by variations of the 
refractive index, the reflection coefficient of open 
sea surfaces, and radar cross sections of ship and 
airplane targets. The latter two questions were being 
undertaken by NRL, and the former was believed 
possible of solution by BTL. 

The business matters of improved liaison with 
Pacific theaters and of the budget for the ensuing 
period were also taken up. 

At other meetings held during January 1945, 
organizational, personnel, and equipment matters 
were taken up and settled as facilities permitted. 
Dr. Carroll, of the War Department Radio Propaga¬ 
tion Section, was appointed a Committee member on 
January 12. Possible cooperation with China was 
discussed, following a discussion by Dr. P. C. T. 
Kwei of Wuhan University, of research carried on in 
China before and during the retreat from the 
Japanese invasion. 

During the month of February the Committee on 
Propagation established liaison with the Watson 
Laboratories of the Army Air Force which Jiad 
recently begun operations. 

In February also the Committee heard an address 
by Dr. S. K. Mitra of the Council of Scientific and 
Industrial Research in India and established liaison 
with that body. 

The question of utilizing the services of Dr. Kwei 
and his assistant, Dr. Eugene Hsu, in obtaining 
ionospheric information after their return to China 
was also discussed. 

On March 6, 1945, a detailed report by Dr. Carroll 
on uses of tropospheric propagation in the Army 
was submitted to the Committee. This report had 
been prepared during January and provided a great 
deal of information needed by the Committee in 
continuing the propagation investigation. At later 
meetings in March, the matter of utilizing the 
services of Dr. Kwei and Dr. Hsu was settled affirma¬ 
tively, and a meeting was held with representatives 
of the Coast Guard to establish a better liaison 
link with that service. 

Martin Katzin of NRL was appointed a Committee 
member early in April. Later that month the 
Chairman prepared a report for Col. D. N. Yates, 
Chief of the Weather Division, AAF, on the problems 




COMMITTEE ACTIVITIES 


21 


involved in correcting existing errors in fire control 
radars, due to refractive effects. 

The fourth conference on propagation was held 
in Washington in May 1945. This conference was 
the largest and most comprehensive yet held and 
was attended by 236 representatives of about 59 
separate agencies of the Allied Nations. A report of 
this conference was published as usual by the 
CUDWR WPG and distributed through authorized 
channels. A great deal of important data was pre¬ 
sented at this conference, including showing of a 
motion picture produced in Britain which presented 
in effective form much information on nonstandard 
propagation, particularly propagation in ducts of 
stratified air layers. Another short motion picture 
prepared in Canada was presented in which radar 
echoes from snowstorms were shown on an acceler¬ 
ated time scale. Progress of such storms was readily 
followed by radar observation, and the importance 
of microwave propagation for this and similar 
applications was made apparent. 

At the close of the conference the chairman 
announced that a contract had been negotiated with 
the Jam Handy Organization for production of a 
motion picture to present pictorially the uses of 
propagation data by the armed forces. 

With the collapse of the enemy in Europe, little 
shifting of the Committee’s program was required. 
The Committee was formed too late in the war to be 
of major help in the European theater so from the 
start the efforts were aimed at the solution of propa¬ 
gation problems of the war in the Pacific the¬ 
ater. 

A meeting late in June 1945 considered advances 
in theoretical methods of attacking the propagation 
problem and agreed on certain standard symbols 
for representing the quantities involved, to avoid 
confusion between investigating agencies. 

Two additional contracts were arranged during 
June, the first with the University of Texas for the 
measurement of variations in angle of arrival of 
microwave radiation under varying meteorological 
conditions. This question has a very direct bearing 
on the troublesome question of improving accuracy 
of radar controlled gunfire, which played such an 
important part in defense against Japanese suicide 
plane attacks. 

The second contract was negotiated with the 
Humble Oil Company on July 2, 1945, for the 
manufacture of a number of field strength measur¬ 
ing equipments which were required by various 


Service agencies of the United States and Allied 
nations. 

A particularly important meeting of the Committee 
took place on July 13 in Washington. This meeting 
was attended by several representatives of the 
Allied Nations, including Professor D. R. Hartree, 
J. M. C. Scott, and Lt. Comdr. F. L. Westwater from 
England, and Drs. Kwei and Hsu from China. The 
progress of the theoretical attack on wave propaga¬ 
tion through a nonhomogeneous atmosphere was 
thoroughly discussed by Prof. Hartree and Dr. C. L. 
Pekeris of the Analysis Section of CUDWR WPG. 

Dr. A. T. Waterman of the Office of Field Service 
reported on work being done in the Southwest 
Pacific by D. E. Kerr. In the investigation of the diffi¬ 
culties of operation of the MEW radar on Saipan he 
confirmed the existence of a low-level evaporation 
duct discovered by Dr. Anderson and Dr. Stephenson 
in that area. Elevated ducts, the presence of which 
had been suspected by Dr. Anderson from analyses of 
radiosonde data, were definitely determined to exist 
at heights ranging from 1,000 to 2,700 ft, as a result 
of Kerr’s investigations. 

Dr. Waterman also described a survey of Service 
interest in scientific developments conducted in the 
entire area commanded by General MacArthur, in 
which a number of ways were found for OSRD to 
assist the Army Air and Ground Forces. The Pacific 
Branch of OSRD was organized so as to furnish a 
consulting staff under a director, a pool of scientists 
available for emergency field work, and a laboratory 
for solution of emergency field problems. This work 
was to be under directorship of Dr. K. T. Compton, 
and it seemed very desirable to have a representative 
in close touch with this OSRD unit in the field. 

Dr. Anderson stressed the importance of conduct¬ 
ing additional research in the Southwest Pacific area, 
and the need for informing the Services in that 
theater more fully of the operational advantages to 
be gained directly from such research. He went on 
to report progress in development and production 
of the equipment developed under the State College 
of Washington contract for making atmospheric 
soundings. 

Lt. Comdr. Westwater reported on the overland 
propagation experiment going on at Suffield, Alberta, 
which was not yet completed, and described the 
meteorological conditions obtaining along the trans¬ 
mission path. These were of the type producing 
variations in the vertical angle of arrival of micro- 
wave radiation transmitted at angles near the hori- 




22 


CHRONOLOGICAL RECORD 


zontal, and Dr. Burrows suggested that this experi¬ 
ment might be integrated with the Committee’s 
angle-of-arrival project for determining refractive 
errors in gun-laying radar systems. 

Methods for taking atmospheric soundings were 
reviewed, and a new combination kite and balloon 
was described in a report by M. Katzin of NRL. 

Dr. Carroll reported on extensive tests on prac¬ 
tically all types of VHF military voice communica¬ 
tion sets, which were being planned in California. He 
reported that radio propagation tests were going to 
be correlated with meteorological measurements 
made with wired sondes. 

The appointment of Dr. Kwei as the Committee’s 
representative in China was discussed, and Dr. Kwei 
described the communication facilities to be made 
available for handling ionospheric propagation data 
obtained in China for transmission to the Committee. 
He urged that more scientifically trained personnel 
be transported to China when possible, to offset the 
very great lack of such persons to assist in the work. 

Dr. Carroll described experiments going on in 
Florida supplementary to those being conducted in 
California, designed to answer questions about the 
maximum reliable range for VHF communications 
sets under varying conditions. 

Meteorological measurements made offshore in the 
Boston area by the Radiation Laboratory Wave 
Propagation Group were described by Dr. R. B. 
Montgomery. These established the existence of 
ducts and at times substandard layers varying in 
height from 100 to as much as 700 ft, with complex 
distributions of refractive index. These measurements 
were especially important as they were known to 
parallel conditions to be expected in similar regions 
off the North China and Japanese coasts. 

Work in progress on all other projects was also 
discussed, including angle-of-arrival experiments and 
the overland tests going on in New Zealand, Canada, 
and Arizona. Mr. R. J. Hearon reported on the new 
contracts, with particular reference to the direct 
Service interest in each. The whole future of propa¬ 
gation investigation was then considered, particu¬ 
larly with reference to the future employment of the 
propagation group at MIT-RL. It was the opinion of 
some Service representatives that the operation of 
this research establishment should be conducted 
under joint Army-Navy control. It was found impos¬ 
sible to reach definite conclusions as to a program to 
continue after eventual demobilization of OSRD, 
but general opinion was that a contract under the 


Chiefs of Staff or other coordinating group might be 
made with MIT or a similar organization. It was 
decided to continue discussion at the next meeting. 

On July 2, 1945, a summary of projects for 
consideration by the proposed Research Board for 
National Security [RBNS] was prepared for presen¬ 
tation when that body should become active. This' 
included a considerable list of propagation, meteor¬ 
ology, and equipment problems requiring further 
research. At the date of writing, the exact status of 
this proposal with the RBNS is not known. 

With the decisive change in the course of the war 
which took place during July and August 1945, 
emphasis was shifted from operational propagation 
problems to organizational and administrative mat¬ 
ters, particularly reports, demobilization, and recom¬ 
mendations for a continuing program. 

On July 30, a letter was circulated among the 
members and representatives of the Services request¬ 
ing consideration of certain definite questions relating 
to future propagation research and reviewing such 
opinion as had already been expressed on the matter. 
Service interest in a continuing program had already 
been manifested, and it was felt particularly impor¬ 
tant that action be taken before the teams of ideally 
suited research workers at MIT and other labora¬ 
tories were demobilized. 

Upon the Japanese surrender in August 1945, the 
principal efforts of the Committee were directed to 
accomplishing contract terminations, preparation 
and submission of a final report, and demobilization 
of the organization. At a meeting on August 28, the 
matter of contract terminations was settled, and 
additional discussion of future propagation research 
was held. 

A meeting of the Committee on Propagation was 
held in Wishington on October 30, 1945, to discuss 
termination of the various projects and related mat¬ 
ters, including preparation of a Summary Technical 
Report and a history, and the probable future of 
propagation research. This was expected to be the 
last full meeting of the Committee, and a large 
amount of business was transacted which can be 
mentioned only briefly here. The entire membership 
was present, with liaison officers of various Services 
concerned and several representatives of contractors 
and of British and Australian research agencies. 

Dr. Saxton reported that future work in the 
United Kingdom was under discussion but that a de¬ 
cision had not yet been reached. He described certain 
experiments proposed for trial in New Zealand, for 



COMMITTEE ACTIVITIES 


23 


which meteorological equipment was needed, and 
another which might be handled in South Africa. 
He also explained that the Canadian experiments 
along a land path near Suffield, Alberta, were con¬ 
tinuing and that Sir Edward Appleton was of the 
opinion that the Ultra Shortwave Panel in Great 
Britain would continue to function into the peace. 

Dr. Anderson reported that meteorological appa¬ 
ratus consisting of six sets of the lower atmosphere 
sounding apparatus developed at the State College of 
Washington was ready for transfer to New Zealand 
and that about forty sets of castings for the equip¬ 
ment were also available for distribution. 

Mr. Munro announced that propagation research 
was to continue in Australia at the Radio Physics 
Laboratory and that the Radio Propagation Com¬ 
mittee, a subcommittee of the Radio Research Board, 
would continue to function. He described the postwar 
policy for this investigation as favoring an expansion 
of the investigation with transfer of workers from 
projects. Fields of investigation in which work was 
proceeding or planned included tropospheric and 
ionospheric propagation, scattering from clouds and 
layers in the middle atmosphere, and a study of 
radio noise levels. Analysis of Service data was being 
conducted, a report on extra-long range echoes 
observed near Darwin had been issued, and a statis¬ 
tical survey of superrefraction along the Australian 
coast was under preparation. 

Lieutenant W. E. Gordon, AAF, described angle- 
of-arrival measurements being conducted in New 
Jersey by BTL, simultaneously with meteorological 
measurements by the Weather Division of the AAF. 
Angles varying from 0.7 degree above to 0.1 degree 
below the line of sight were observed over the 123^- 
mile path, the nonstandard angles always coinciding 
with measured nonstandard atmospheric refractive 
conditions. On two occasions multiple paths had 
been observed. 

Dr. E. W. Hamlin reported progress of the 
University of Texas group which was to study angle 
of arrival by measuring phase difference. He an¬ 
nounced that the Office of Research and Inven¬ 
tions of the Navy had agreed to take over the 
project on an interservice plan of participation, with 
cooperation of Army and Navy laboratories, and 
active exchange of information with BTL and other 
interested agencies. It was also expected that AAF 
and other field stations would collaborate. 

Dr. W. M. Rush described progress in construction 
of the receivers for field strength measurement under 


the Humble Oil Company contract. Of the 24 units 
scheduled, 18 were to be completed by October 31, 
1945. In addition, he announced that the company 
was interested in geophysical surveys over the Gulf 
to distances of 30 miles offshore by means of radar 
measurements and would be glad to cooperate with 
the University of Texas and Service groups. 

The chairman announced that steps were under way 
to declassify all propagation information and to make 
it feasible for all organizations interested to obtain 
copies of pertinent material published by NDRC. 

Captain D. R. Hull announced that the name of 
the NRSL was shortly to be changed to Navy 
Electronics Laboratory [NEL] and that facilities in 
Arizona were soon to be available for cooperation 
with the University of Texas. 

D.E. Kerr announced the transfer of signal strength 
measuring receivers from RL to NRSL [NEL] and 
went on to describe a field expedition conducted by 
himself for the Operational Research Section of the 
Office of Field Service. He stated that the cause of the 
poor operation of the MEW was poor adjustment of 
the equipment. He confirmed the existence of strong 
superrefraction. He also mentioned contacting a 
part of Dr. Anderson’s group in Manila and de¬ 
scribed the necessity for disseminating knowledge of 
propagation effects among operating personnel in the 
field, particularly in the Army. He also described use 
being made of radar for storm detection by the 
Southwest Pacific Weather Force and a series of 
educational talks being conducted with radar officers 
in the Philippines when the war ended. 

Dr. Carroll briefly described results of propagation 
tests made by the Signal Corps along several over¬ 
water and over-land optical paths in California, on 
100 , 250, 1,450, and 4,500 me. Elevated ducts had 
been observed, but surface reflection was found to 
be of greater importance. General conclusions from 
these tests indicated the importance of reflection 
from sea and land surfaces and the desirability of 
employing diversity reception with antennas spaced 
vertically. 

Dr. Dellinger described his trip to a conference on 
radio held in Brazil, at which two government 
departments of that country had expressed willing¬ 
ness to undertake ionospheric observations in 
cooperation with a world-wide network. These 
departments had requested equipment and instruc¬ 
tions for this work, which were to be supplied. 

M. Katzin of NRL referred to the Antigua experi¬ 
ment completed early in the year and described a 



24 


CHRONOLOGICAL RECORD 


similar experiment planned for the Pacific, employ¬ 
ing a mobile laboratory and aircraft, with combina¬ 
tion one-way and radar transmission. He also men¬ 
tioned that XRL and XRSL XEL were planning a 
rather extensive propagation investigation whieh. 
however, would not interfere with the work planned 
for the Navy at the Unfverrity erf Texas. 

Dr. Beverage announced that the activities of 
Division 15 erf NDRC were to end almost completely 
on October 31. 1945. and added that some projects 
were being transferred to the Services but that no 
propagation studies were active. 

Prof. Attwood announced termination erf the Col¬ 
umbia contract <OEMsr-1207 > as erf October 31 and 
stated that 34 reports had been written under its 
terms, with some still awaiting distribution. He also 
mentioned that the Navy was taking over the Anal¬ 
ysis Section erf the Wave Propagation Group under 
a new contract with Columbia University. 

John Campbell erf the Jam Handy Organization 
described progress in the production erf a film cover¬ 
ing many aspects erf propagation phenomena, which 
was ehie for completion about December 10. 1945. 

Lt. Comelr. W. B. Chadwick elescribed a Navy 
plan for predicting radar propagation conditions up 
to 24 hours in advance and transmitting such infor¬ 
mation with measured If curves to a central station 
fen correlation and dissemination. He was erf the 
opinion that the end of the war would probably hah 
this project, making it necessary to return the 
matter to research groups. 

Lt. CoL J. J. Slattery and K. A- Norton announced 
that the Signal Corps planned to extend and continue 
propagation experimentation in general, in coopera¬ 
tion with other Services and industrial and scientific 
establishments. 

The chairman requested comment on projected 
future propagation studies. 

Dr. Dellinger stated that many questions yet to be 
answered seemed appropriate for investigation by a 
national research organization and by the new elec¬ 
tronics department of MIT. He added that there 


was an organization, the Union Radio Scientifique 
Internationale, with Sir Edward Appleton as inter¬ 
national chairman and hims elf as chairman erf the 
American section, which would exercise a definite 
interest in the propagation field. 

D. E. Kerr expressed the opinion that MIT would 
not be in a position to undertake as large a program 
as had been suggested and added that after current 
projects were closed there would still be on hand a 
large amount of unanalyzed data, which could not 
be used unless an agency were found to make the 
analysis. 

Major Wexler announced that the Army Weather 
Service would continue to cooperate with groups 
making propagation measurements and added that 
the Air Force was negotiating through the Signal 
Corps for basic research in storm detection by radar 
to be done at MIT. 

The chairman announced that in view erf the end 
of hostilities, no new conference on propagation 
would be called by the Committee. Following a vote 
of thanks to the Chairman proposed by Dr. Dellinger 
the meeting was adjourned. This was the last full 
meeting held by the Committee, but members re¬ 
mained active for a considerable time longer, carry¬ 
ing on the necessary work of demobilizing the 
organization. 

With general demobilization of the Committee 
imminent and terminations of contracts already 
taking effect, the principal work of the Committee 
was concluded. After termination of the Columbia 
contract, it was felt advisable to appoint Prof. Att¬ 
wood a consultant to the Committee to assist with 
final solution of administrative questions, and this 
was made effective November 1. 1945. An office for 
conducting correspondence and preparing this report 
was maintained in the Empire State Building in 
New York City, under the auspices of the NDRC 
Summary Reports Group. With submiaaon of this 
report for publication, the work of the Committee 
may be considered closed. 







Chapter 4 

RESULTS AND RECOMMENDATIONS 


1-1 RESULTS 

a xt tabulation of the results of the Committee's 
work must be based to a degree on certain 
intangibles difficult to evaluate. This is because a 
substantial proportion of the overall result was a 
change in the attitude of agencies and personnel 
concerned with the performance of radar and radio 
equipment using the frequencies above about 30 me. 
The complete analysis and understanding of propa¬ 
gation of these frequencies through the troposphere 
still lies in the future and will undoubtedly require 
much additional experimental and theoretical work, 
conducted without the restrictions of wartime secrecy 
and urgency. However, a considerable overall tangible 
result was also achieved, both in establishing the 
basic theory of tropospheric propagation and 
in development of methods and instruments for 
measuring meteorological factors influencing such 
propagation. 

In the earlier stages of the war. nonstandard (at 
first called “anomalous”) propagation caused several 
confusing and disconcerting incidents, due to misun¬ 
derstanding of the phenomena. The instance later 
called “The Battle of the Pips.” which took place 
near the Aleutians, was paralleled in other theaters 
many times. In this case echoes returned from 
islands ordinarily beyond radar range caused such 
confusion that fire was opened and an attempt made 
to engage nonexistent enemy units. Such puzzling 
and exasperating variations in radar and radio 
performance caused serious loss of confidence in 
equipment and was of considerable operational sig¬ 
nificance. This has been considered more fully in 
Chapter 1, as it was directly related to the origin 
of the Committee. 

The general effect of such publications as Varia¬ 
tions in Radar Corerage, of which upwards of 30.000 
copies were distributed. Tropospheric Propagation 
and Radio Meteorology . and numerous other reports 
prepared and distributed for the Committee by the 
Columbia University Division of War Research 
[CUDWR] Wave Propagation Group [WPG] under 
contract OEMsr-1207, was to restore confidence in 
the equipment and its use and to focus attention on 
other causes of unreliability, which previously were 


often masked by or confused with the effects of 
propagation variations. These other sources of vari¬ 
able performance, principally misadjustment of or 
defects in equipment caused by the rigors of field 
service, became easier to track down and eliminate, 
because they could be distinguished from propaga¬ 
tion effects with reasonable success when the latter 
were understood. 

Another general result of the Committee’s work 
was a considerable modification of siting principles 
for radar and radio equipment The results of the 
Caribbean over-water experiment, and of similar 
tests conducted at San Diego. Cape Cod, and across 
the Irish Sea, conclusively demonstrated the frequent 
existence of relatively stable horizontal layers of the 
lower atmosphere, in which the vertical distribution 
of refractive index was such as to cause substantial 
departures of actual radar coverage and radio com¬ 
munication range from the values obtained in a 
standard atmosphere. In particular, it was deter¬ 
mined that, over much of the tropical and semi- 
tropical areas of the oceans, such layers were prevalent 
during many months, varying in thickness and 
intensity with wind speed and other measurable 
meteorological variables. These surface layers often 
produced large increases in radar ranges on surface 
craft and low-flying aircraft for radars of appropriate 
frequency sited in or close above the duct. 

These investigations also revealed that under 
certain conditions a reverse effect could occur, in 
which the radiation was refracted downward much 
less than in a standard well-mixed atmosphere, with 
the result that coverage was less than normal. In 
extreme cases the radiation might even be bent 
upward away from the surface, resulting in ranges 
less than optical. In the course of arriving at these 
general results, methods and instruments for measur¬ 
ing the meteorological factors producing these effects 
were developed, particularly the Massachusetts 
Institute of Technology [MIT] psychrograph and 
the State College of Washington [WSC] wired sonde, 
with techniques for interpreting the data in approxi¬ 
mate terms of radar performance. These instruments 
and techniques were made available to the armed 
forces of the Allied Nations. 

A total of about 550 reports on various aspects of 


25 


26 


RESULTS AND RECOMMENDATIONS 


the propagation problem were received from the nu¬ 
merous investigating laboratories. These reports were 
analyzed and the essential information contained 
was put into forms suitable for the use of operational 
personnel and distributed to the Services of the 
. United States and the other Allied Nations. Such 
dissemination usually was in the form of publications 
by the CUDWR WPG, which issued a total of 34 
such reports to a large distribution list. These reports 
and the very much larger number of scientific papers 
from which they were prepared are listed in the 
Bibliography. 

4.2 CRITIQUE 

The greatest handicap to the work of the Committee 
on Propagation was the delay in recognizing the need 
for such an organization. In the rush to get elec¬ 
tronic equipment that would allow the realization 
of the many new war inventions, the fact that the 
tactical use of these equipments depends upon their 
quantitative performance, which in turn depends 
upon the transmission medium, was neglected. As a 
result when this need was finally recognized the few 
experts in this field were deep in important war work 
and the committee decided to work with existing 
laboratories, letting new contracts for specific proj¬ 
ects rather than setting up a central laboratory late 
in the war. The work of the committee should have 
begun with the conception of the ideas of the new 
radio systems, radar, loran, VHF (very high fre¬ 
quency) communication systems, guided missiles, etc. 
Then there would have been time to have established 
a central laboratory for carrying out propagation 
research and evaluating the performance charac¬ 
teristics of equipment. 

4.3 FUTURE PROPAGATION RESEARCH 

During the latter part of 1943, Committee members 
and liaison officers gave considerable attention to the 
matter of propagation research which would be desir¬ 
able to have continued into the postwar period. 
Studies were made of the knowledge already obtained 
with a view to outlining the principal gaps in that 
knowledge and developing a general program for 
filling them, which could be carried on by such 
organizations as the Service laboratories or the 
Research Board for National Security. The results 


of these studies are given here, divided roughly 
into suitable categories. 

Propagation Problems 

1. Subnormal propagation through fog and sus¬ 
pended water and ice particles. 

2. Modifications of the coverage diagram when 
the radiation source is located in or below the hori¬ 
zontal layer exhibiting nonstandard variations of 
refractive index with height. 

3. Errors produced in operation of direction 
finders, navigational equipment, and gunlaying radar 
by varying factors of tropospheric propagation. 

4. Effects on atmospheric reflection of variations 
of frequency, pulse rate, pulse length, radiated power, 
and other variable parameters. 

5. Correlation of variations of horizontal and 
vertical angle of arrival of radio waves with simul¬ 
taneous meteorological measurements and evaluation 
of resulting variations in propagation characteristics. 

6. Determination of frequencies permitting great¬ 
est security under various meteorological conditions. 

7. Measurements of absolute signal strength and 
characteristics of the transmitted signal. 

8. Determination of atmospheric noise levels in 
all important regions and the variation with season, 
frequency, and meteorology. 

9. Phenomena responsible for long distance propa¬ 
gation in the 100- to 200-mc region. 

10. Characteristics of propagation in the region 
between 50 and 500 kc. 

11. Tropospheric propagation measurements over 
various types of terrain and water surfaces to deter¬ 
mine, more accurately, coverage, angle of arrival, 
reflection, scattering, and absorption over the range 
in which the refractive index of the troposphere 
shows significant change. 

12. Further theoretical analysis of propagation 
phenomena and comparison with observed experi¬ 
mental results. 

Meteorological Problems 

1. Particle sizes and distribution for all forms of 
atmospheric water. 

2. Survey of the Pacific area similar to the German 
Meteor study of the Atlantic. 

Equipment Problems 

1. Development of improved equipment for measur¬ 
ing variations of atmospheric refractive index. 

2. Development of improved equipment for gener- 



FUTURE PROPAGATION RESEARCH 


27 


ating, detecting, and measuring radiation in the part 
of the frequency spectrum under consideration. 

3. Required field strengths necessary for satisfac¬ 
tory operation of systems employing this range of 
frequencies. 

4. Types of equipment suitable for determining 
location, intensity, and movement of storms, and 
distinguishing them from permanent echoes. 

5. Handbooks of standard and nonstandard propa¬ 
gation and of standard performance of radar equip¬ 
ment. 

Some of the points listed are not strictly propa¬ 
gation questions, but their investigation will require 


the active assistance of propagation experts for 
solution. It is expected that systematic investigation 
will do much to eliminate the factors of uncertainty 
in siting and operation as well as in design of radio 
equipment operating in the frequency bands con¬ 
sidered, particularly when better methods and 
apparatus have been developed for determining the 
performance of the equipment itself. Such methods 
and apparatus were by no means satisfactory during 
the war, with the result that uncertainty as to the 
actual condition and performance of equipment in 
the field further complicated the already formidable 
problem of determining propagation characteristics. 










PART II 


SUMMARY 








Chapter 5 

STANDARD PROPAGATION 


51 INTRODUCTION 

B y standard propagation is meant radio wave 
propagation through an atmosphere free from 
irregular stratifications, particularly of vertical dis¬ 
tributions of water vapor and temperature. With 
irregular stratification the propagation is said to be 
nonstandard and will be treated extensively in the 
later chapters. 

In this chapter the fundamental general relations 
between transmitted and received power is first re¬ 
viewed; then the main factors influencing the trans¬ 
mission of electromagnetic waves such as refraction, 
diffraction, and dielectric properties of the ground 
are surveyed; and finally the computation of the 
field at the receiver for various heights of transmitter 
and receiver above a homogeneous smooth earth of 
given electromagnetic properties is very briefly dis¬ 
cussed. The last subject divides naturally into the 
determination of the field above the line of sight and 
the determination of the field below the line of sight 
in the earth’s shadow. 

The text of the present chapter largely follows the 
book, issued by the Columbia University Wave 
Propagation Group [CUDWR WPG] under the title 
Propagation of Radio Waves through the Standard 
Atmosphere which is Volume 3 of the Summary 
Technical Report of the Committee on Propagation. 


52 POWER TRANSMISSION 

Certain relations occur so frequently in wave 
propagation problems that it is convenient to 
summarize them here before entering into a descrip¬ 
tion of the characteristic features of short wave 
propagation. Some of these are mere definitions; 
some are consequences of electromagnetic theory. 

It is convenient to use, as a standard antenna, one 
which has a length which is small compared to the 
wavelength, designated as “doublet.” Such doublets 
may be used for both the transmitting and receiving 
antennas. In the latter case it is assumed that the 
load resistance is matched to the output resistance 
of the antenna. In free space, optimum transmission 
is achieved when the two doublets are parallel to 


each other and perpendicular to the line connecting 
their centers. If their distance apart, d, is large com¬ 
pared to the wavelength, the ratio of power trans¬ 
mitted to maximum useful power received is found 
from electromagnetic theory to be 



where X and d are measured in the same units. Here 
P 2 is the power delivered to a matched load at the 
output terminal of the receiver and P x the power fed 
to the transmitting antenna. 

The gain G of any directive antenna is the ratio of 
the power transmitted by a doublet to the power 
transmitted by the antenna in question, to produce 
the same response in a distant receiver, when both 
transmitting antennas are adjusted for maximum 
transfer of power. The gain of a receiving antenna is 
similarly the ratio of the power delivered to the 
transmitting antenna when a doublet receiving an¬ 
tenna is used to the power delivered to the transmit¬ 
ting antenna to produce the same response when the 
antenna in question is used at the receiver. 

Two methods of expressing antenna gain are in 
common use: the one just indicated where the gain 
is measured as the ratio of the power in the optimum 
direction relative to that of a doublet, and the other 
where the gain is that relative to a hypothetical iso¬ 
tropic radiator which is one assumed to radiate the 
same power density in all directions. Simple geomet¬ 
rical considerations show that the gain of a doublet 
over that of an isotropic radiator is 3/2 so that the 
gains expressed in the former system are converted 
into the latter system by multiplying them by 3/2. 
In the equations below, the gain is expressed relative 
to the doublet. 

If transmission takes place, not in free space, but 
over a conducting ground, in a refracting atmosphere, 
etc., the power ratio will be expressed as 

r, - ’ <2) 

where G 1 G 2 are the antenna gains of the transmitting 
and receiving systems, respectively, and A p is the 


31 


34 


STANDARD PROPAGATION 



Figure 4. Phase lag, </>, of the reflection coefficient 
versus reflection angle, xf/, from = 0 to = 5.5° for 
sea water. 


about 12 degrees with moist soil and at about 21 
degrees with dry soil. 

For the ocean surface, and vertical polarization, 
the imaginary part of the dielectric constant cannot 
be neglected, and the reflection coefficient as a func¬ 
tion of the angle does not vanish at any angle but 
goes through a minimum, the pseudo-Brewster angle. 
The actual variation of amplitude and phase lag is 
represented in Figures 2 and 3 for the small angles of 
reflection which are most important in practice. 

When the ground is rough the reflection coeffi¬ 
cient for both types of polarization is reduced to a 
very small value. For 10-cm waves and still more for 
shorter ones, most types of land are rough. A reflec¬ 
tion coefficient of 0.2 may be taken as representative 
for an average ground covered with vegetation. A 
slightly ruffled sea is a fairly good reflector for 10-cm 
waves but appears somewhat rough at shorter wave¬ 
lengths. 

Standard Refraction 


From the practical viewpoint the following sum¬ 
mary may give an overall picture of the more out¬ 
standing features of ground and sea reflection. 

For horizontal polarization over the sea the reflec¬ 
tion coefficient may be taken as unity and the phase 
shift as 180 degrees for frequencies up to and includ¬ 
ing the centimeter range, for practically all angles of 
reflection. Over land there is a slight decrease of the 
amplitude of the reflection coefficient with increasing 
angle; for instance, for a frequency of 200 me, at 
an angle of 15 degrees the reflection coefficient has 
decreased to 0.9 or slightly more for moist soil and 
to 0.8 or slightly more for dry soil. These statements 
apply when the ground or sea surface is reasonably 
smooth. In order to decide whether a surface is 
smooth or rough, Rayleigh’s criterion, explained 
below, is usually applied. When the surface is rough 
or wavy, irregular scattering predominates and re¬ 
duces the intensity to a small part of the value 
attained with a smooth surface. 

For vertical polarization the curve of the magnitude 
of the reflection coefficient versus the angle goes 
through a minimum (see Figure 2). When the imagi¬ 
nary term of the complex dielectric constant is 
negligible so that the ground behaves like a pure 
dielectric material, the reflection coefficient goes to 
zero at a certain angle (Brewster angle). Ordinary 
soil nearly fulfills this condition. For instance, at a 
frequency of 200 me the Brewster angle occurs at 


Numerous experiments have resulted in the fol¬ 
lowing formula for the refractive index of moist air: 

(» - 1) • 10 6 =* ( p - e + nr 5 ) (9) 

where n = the index of refraction, 

p = the barometric pressure in millibars 
(1 mm mercury = 1.3332 mb), 
e — partial pressure of water vapor in milli¬ 
bars, 

T = absolute temperature. 

The mixing ratio, s, which is practically equal to 
specific humidity, is connected with e by the relation 

e = 0.00161ps . (10) 

A recent analysis 278 has shown, moreover, that this 
expression for refractive index must, on theoretical 
grounds, be substantially independent of frequency 
down to the shortest waves employed in microwave 
engineering. 

In an average atmosphere temperature, pressure, 
and water vapor density decrease with height, and, 
in the lowest few kilometers where most of the short 
and microwave propagation takes place, it may be 
assumed to a good approximation that the decrease 
of refractive index with height is linear though the 
rate of decrease is somewhat dependent on the cli¬ 
mate. In middle latitudes it is given by 



























































OPTICAL PROPERTIES OF THE EARTH’S SURFACE AND ATMOSPHERE 


35 


^ = —0.039 • 10 -6 per meter . (11) 

Refraction at the boundary of two media is fa¬ 
miliar from optics and is expressed by Snell's law: 

tti cos ai = n 2 cos a* , (12) 

where n x and n 2 are the refractive indices of the two 
media and a x and a 2 the angle between the boundary 
and the direction of the ray in the first and second 
media respectively. In the atmosphere the refrac¬ 
tive index is a continuous function of height, and the 
sudden change of direction at a boundary is then 
replaced by a curvature of the rays. Equation (12) 
can be written 


atmosphere involved. This has the advantage of per¬ 
mitting a close fit with observed refractive index 
curves up to heights of 6 to 8 km. It seems, however, 
that the advantage of the greater analytical simplic¬ 
ity of the linear refractive index curves far outweighs 
the increased accuracy of the quadratic form, and the 
latter has therefore not found acceptance in this 
country and Great Britain. 

It is customary to designate the effective, or modi¬ 
fied earth radius by ka where k is a numerical con¬ 
stant and a replaces r 0 used above and represents 
the mean radius of the earth. Hence 


n cos a = n Q cos a 0 , (13) 

where n and a are now continuous functions of the 
height and the subscript 0 designates a reference level. 

The above formulas refer to a plane earth. If the 
earth's curvature is taken into account so that the 
planes relative to which the angle a is measured are 
replaced by spheres about the earth’s center, for¬ 
mula (13) must be modified; and the mathematical 
analysis shows 442 that it is replaced by 

nr cos a = n 0 r 0 cos « 0 (14) 

where r is the distance from the center of the earth 
to the level considered. 

If now we set r = r 0 (1 + h/r 0 ) where h = r — r 0 
and h/r 0 is a small quantity and, furthermore, if we 
note that with a linear gradient of n 

n = n ° + M h (15) 

we obtain on substituting into (14) and neglecting 
small quantities of the second order 

1 + (-y -f* ( ^J /ij cos a = cos a 0 . (16) 

It results from this equation that a linear gradient 
of refractive index has the same effect on refraction 
as the curvature of the earth, l/r 0 . By introducing 
an effective earth's radius it is possible to eliminate 
the refraction term entirely and to treat the atmos¬ 
phere as if it were homogeneous. This device was first 
introduced by Schelleng, Burrows, and Ferrell, 24 and 
has since been generally accepted. Some German 
writers have introduced a quadratic function to 
represent the variation of refractive index with height 
in the atmosphere, 443 the coefficients of the quadratic 
terms being characteristic of the air mass or type of 


and by comparison with equation (11) it follows that 

k = | (18) 

since dn/dh = — 0.039 • 10 6 = — l/4a. The earth’s 
radius a = 6.37 • 10 6 meters. 

In view of this result coverage diagrams of radar 
and radio communication sets are commonly drawn 
with a % earth’s radius. In such a diagram the rays, 
which are curved in a “true” geometric representa¬ 
tion, appear as straight lines. 

The value k = % does not, of course, represent a 
universal law. It is merely an expression of the fact 
that the rate of decrease of the refractive index with 
height has, in the middle geographical latitudes, a 
certain average value. In arctic climates fc as a rule 
is somewhat smaller, lying between % and %, while 
in tropical climates k is somewhat larger, between 
Ys and %. In temperate and tropical climates, the 
main factor determining the magnitude of k is the 
humidity gradient in the lower atmosphere. In 
Figure 5 is shown a nomogram from which the ap¬ 
propriate value of 1/k can be read directly as function 
of the gradient of relative humidity and air tempera- 
ature. The table has been computed under the as¬ 
sumption that the temperature gradient has the 
“standard” value of —0.65 C per 100 m, but the 
value of k is relatively insensitive to variations in 
the temperature gradient. 

Usually the value of k = % is referred to as the 
standard case, but this term is also used to designate 
more generally an atmosphere with a linear refrac¬ 
tive index distribution where k might differ somewhat 
from %. Experience shows that the atmospheric 
conditions under which the refractive index is a 
linear function of height are quite common, but this 



34 


STANDARD PROPAGATION 



Figure 4. Phase lag, <f>, of the reflection coefficient 
versus reflection angle, \f/, from \J/ = 0 to \J/ — 5.5° for 
sea water. 


about 12 degrees with moist soil and at about 21 
degrees with dry soil. 

For the ocean surface, and vertical polarization, 
the imaginary part of the dielectric constant cannot 
be neglected, and the reflection coefficient as a func¬ 
tion of the angle does not vanish at any angle but 
goes through a minimum, the pseudo-Brewster angle. 
The actual variation of amplitude and phase lag is 
represented in Figures 2 and 3 for the small angles of 
reflection which are most important in practice. 

When the ground is rough the reflection coeffi¬ 
cient for both types of polarization is reduced to a 
very small value. For 10-cm waves and still more for 
shorter ones, most types of land are rough. A reflec¬ 
tion coefficient of 0.2 may be taken as representative 
for an average ground covered with vegetation. A 
slightly ruffled sea is a fairly good reflector for 10-cm 
waves but appears somewhat rough at shorter wave¬ 
lengths. 

Standard Refraction 


From the practical viewpoint the following sum¬ 
mary may give an overall picture of the more out¬ 
standing features of ground and sea reflection. 

For horizontal polarization over the sea the reflec¬ 
tion coefficient may be taken as unity and the phase 
shift as 180 degrees for frequencies up to and includ¬ 
ing the centimeter range, for practically all angles of 
reflection. Over land there is a slight decrease of the 
amplitude of the reflection coefficient with increasing 
angle; for instance, for a frequency of 200 me, at 
an angle of 15 degrees the reflection coefficient has 
decreased to 0.9 or slightly more for moist soil and 
to 0.8 or slightly more for dry soil. These statements 
apply when the ground or sea surface is reasonably 
smooth. In order to decide whether a surface is 
smooth or rough, Rayleigh’s criterion, explained 
below, is usually applied. When the surface is rough 
or wavy, irregular scattering predominates and re¬ 
duces the intensity to a small part of the value 
attained with a smooth surface. 

For vertical polarization the curve of the magnitude 
of the reflection coefficient versus the angle goes 
through a minimum (see Figure 2). When the imagi¬ 
nary term of the complex dielectric constant is 
negligible so that the ground behaves like a pure 
dielectric material, the reflection coefficient goes to 
zero at a certain angle (Brewster angle). Ordinary 
soil nearly fulfills this condition. For instance, at a 
frequency of 200 me the Brewster angle occurs at 


Numerous experiments have resulted in the fol¬ 
lowing formula for the refractive index of moist air: 

( i\ 1A6 79 / . 4,800e\ , . 

(n - 1) • 10 6 = ( p - e + ( 9 ) 

where n = the index of refraction, 

p = the barometric pressure in millibars 
(1 mm mercury = 1.3332 mb), 
e = partial pressure of water vapor in milli¬ 
bars, 

T = absolute temperature. 

The mixing ratio, s, which is practically equal to 
specific humidity, is connected with e by the relation 

e = O.OOlGlps . (10) 

A recent analysis 278 has shown, moreover, that this 
expression for refractive index must, on theoretical 
grounds, be substantially independent of frequency 
down to the shortest waves employed in microwave 
engineering. 

In an average atmosphere temperature, pressure, 
and water vapor density decrease with height, and, 
in the lowest few kilometers where most of the short 
and microwave propagation takes place, it may be 
assumed to a good approximation that the decrease 
of refractive index with height is linear though the 
rate of decrease is somewhat dependent on the cli¬ 
mate. In middle latitudes it is given by 










































OPTICAL PROPERTIES OF THE EARTH’S SURFACE AND ATMOSPHERE 


35 


—r = —0.039 • 10~ 6 per meter . (11) 

clh 

Refraction at the boundary of two media is fa¬ 
miliar from optics and is expressed by Snell's law: 

U\ cos q'i = n 2 cos a 2 , (12) 

where n i and n 2 are the refractive indices of the two 
media and on and a 2 the angle between the boundary 
and the direction of the ray in the first and second 
media respectively. In the atmosphere the refrac¬ 
tive index is a continuous function of height, and the 
sudden change of direction at a boundary is then 
replaced by a curvature of the rays. Equation (12) 
can be written 


atmosphere involved. This has the advantage of per¬ 
mitting a close fit with observed refractive index 
curves up to heights of 6 to 8 km. It seems, however, 
that the advantage of the greater analytical simplic¬ 
ity of the linear refractive index curves far outweighs 
the increased accuracy of the quadratic form, and the 
latter has therefore not found acceptance in this 
country and Great Britain. 

It is customary to designate the effective, or modi¬ 
fied earth radius by ka where k is a numerical con¬ 
stant and a replaces r 0 used above and represents 
the mean radius of the earth. Hence 


n cos a = n 0 cos a 0 , (13) 

where n and a are now continuous functions of the 
height and the subscript 0 designates a reference level. 

The above formulas refer to a plane earth. If the 
earth's curvature is taken into account so that the 
planes relative to which the angle a is measured are 
replaced by spheres about the earth’s center, for¬ 
mula (13) must be modified; and the mathematical 
analysis shows 442 that it is replaced by 

nr cos a = n 0 r 0 cos a 0 (14) 

where r is the distance from the center of the earth 
to the level considered. 

If now we set r = r 0 (1 + h/r 0 ) where h = r — r 0 
and h/r 0 is a small quantity and, furthermore, if we 
note that with a linear gradient of n 

7i = n 0 + h (15) 

we obtain on substituting into (14) and neglecting 
small quantities of the second order 

1 + -f- cos a = cos ao . (16) 

It results from this equation that a linear gradient 
of refractive index has the same effect on refraction 
as the curvature of the earth, l/r 0 . By introducing 
an effective earth's radius it is possible to eliminate 
the refraction term entirely and to treat the atmos¬ 
phere as if it were homogeneous. This device was first 
introduced by Schelleng, Burrows, and Ferrell, 24 and 
has since been generally accepted. Some German 
writers have introduced a quadratic function to 
represent the variation of refractive index with height 
in the atmosphere, 443 the coefficients of the quadratic 
terms being characteristic of the air mass or type of 


and by comparison with equation (11) it follows that 

k = | (18) 

since dn/dh = — 0.039 • 10 6 = — l/4a. The earth’s 
radius a = 6.37 • 10 6 meters. 

In view of this result coverage diagrams of radar 
and radio communication sets are commonly drawn 
with a /3 earth’s radius. In such a diagram the rays, 
which are curved in a “true” geometric representa¬ 
tion, appear as straight lines. 

The value k = % does not, of course, represent a 
universal law. It is merely an expression of the fact 
that the rate of decrease of the refractive index with 
height has, in the middle geographical latitudes, a 
certain average value. In arctic climates A; as a rule 
is somewhat smaller, lying between % and %, while 
in tropical climates k is somewhat larger, between 
% and %. In temperate and tropical climates, the 
main factor determining the magnitude of k is the 
humidity gradient in the lower atmosphere. In 
Figure 5 is shown a nomogram from which the ap¬ 
propriate value of 1 /k can be read directly as function 
of the gradient of relative humidity and air tempera- 
ature. The table has been computed under the as¬ 
sumption that the temperature gradient has the 
“standard” value of —0.65 C per 100 m, but the 
value of k is relatively insensitive to variations in 
the temperature gradient. 

Usually the value of k = % is referred to as the 
standard case, but this term is also used to designate 
more generally an atmosphere with a linear refrac¬ 
tive index distribution where k might differ somewhat 
from %. Experience shows that the atmospheric 
conditions under which the refractive index is a 
linear function of height are quite common, but this 



36 


STANDARD PROPAGATION 


(RH) q -3qc -25C -20C -15C -1QC 

,027 .039 


7oi2":oT7 

.011 .015 
.009 .OH 
.008 .012 
.007 .010 
.005 .008 
.004 -006 
.003 .004 
.001 .002 


.024 .034 
,021 .030 
018 .026 
,015 .021 
,012 .017 
009 .013 
006 .009 
003 .004 


-5C PC 

,055 .078 

,049 .069 
,043 .060 
,037 .052 
031 .043 
024 .034 
018 .026 
012 .017 
006 .009 


+5C +10C 

090 .113 

080 .105 
070 .092 
060 .079 
050 .066 
040 .052 
030 .039 
020 .026 
010 .013 



267 .329 
.234 .288 
.200 .247 
.167 .206 
.134 .165 
.100 .123 
.067 .082 
.033 .041 



Figure 5. Graph: 1/A; versus RH gradient and temperature for 100 per cent RH at ground. Add correction tabulated to 
obtain 1/A; for RH at ground 7^ 100%. 


is only one case out of several that may, and do, 
arise in the atmosphere. A full appreciation of the 
limitations of the concept of standard refraction 
requires some knowledge of the phenomena of non¬ 
standard propagation which will be dealt with ex¬ 
tensively in later chapters. 

Roughness of the Ground 

In order to estimate how closely the ground ap¬ 
proximates the condition of an ideal reflecting sur¬ 
face, a rule is required that gives results sufficiently 
accurate to be used in radio and radar practice. The 
subject has not been very thoroughly explored, but 
Rayleigh’s criterion for roughness, originally devel¬ 
oped for optical purposes, has been applied with good 
success. Since it seems to be the only criterion of its 
kind and since it is often necessary to decide whether 
the terrain in front of a given radio or radar site is 
reflecting, it deserves some detailed consideration. 

The principle of Rayleigh’s criterion is illustrated 
in Figure 6. The roughness is assumed to be pro¬ 
duced by a large number of elevations in the reflect¬ 
ing plane of average height H. One such “hump” 


is shown in the figure together with two rays one of 
which is assumed to be reflected from the ground sur¬ 
face and one from the top of the “hump.” The dif¬ 
ference in phase between the two rays is 2//^(27 t/\). 



Figure 6. Geometry for Rayleigh’s criterion for rough 
ground. 


The criterion now requires that the surface be con¬ 
sidered as rough when this phase difference exceeds 
7 t/ 4 radians. This gives for the critical value of H, 
when \p is in degrees, X in meters, 


If n is the “lobe variable,” that is, a quantity equal 
to 1, 3 • • • (2 n — 1), • • • at the first, second, 






























































































OPTICAL PROPERTIES OF THE EARTH’S SURFACE AND ATMOSPHERE 


37 


nth interference maximum of the direct and ground- 
reflected rays, namely, 


n = 


X ’ 


( 20 ) 


where hi is the height of the transmitter above the 
ground, the criterion can be written in the form 



( 21 ) 


Although admittedly rough, the criterion indicates 
the order of magnitude of the angle above which 
specular reflection will be greatly reduced in favor 
of diffuse scattering of the type which, in ordinary 
optics, is produced by a dull, white surface. It is 
reasonably safe to assume that for angles exceeding 
the critical angle the amount of specular reflection 
will be reduced to a small fraction, perhaps to the 
order of one-fifth, of the value of the reflection under 
ideal conditions. 


Diffraction by Terrain 

A number of the influences of the earth’s surface 
upon wave propagation have the common charac¬ 
teristic that they represent deviations of the actual 
earth from the idealized model of a smooth sphere 
endowed with homogeneous electrical constants. 
Diffraction by the earth’s average curvature is not 
included among the effects considered here since it 
is dealt with extensively in Vilume 3. 

There are two main classes of phenomena that fall 
under the general heading of diffraction. One is the 
diffraction by obstacles, such as hills, trees or houses, 
and the other is the diffraction by the structure of 
an otherwise fairly level ground, in particular, rough¬ 
ness and horizontal variations of dielectric constant. 

The diffraction by hills and similar obstacles of the 
terrain is commonly treated theoretically by means 
of the Fresnel-Kirchhoff diffraction theory as found 
in textbooks on optics. The only problem which is 
sufficiently simple to admit of a direct application to 
short wave transmission is that of diffraction by a 
straight edge. It is not necessary that the edge be 
perpendicular to the line connecting the transmitter 
and receiver but for the validity of the theory it is 
necessary to suppose that the distances from the 
diffracting obstacle to the transmitter and receiver 
are large compared to the height of the obstacle, 
which means that the angles of diffraction are small. 



Figure 7. Field in shadow behind a diffracting ridge. 


Figure 7 shows a nomogram from which the field 
strength in the shadow of a diffracting edge can be 
read in decibels below that of free space. The geo¬ 
metrical significance of the quantities used is illus¬ 
trated on the figure. 

Such experiments as have been made show a gen¬ 
eral agreement with theory, but it is difficult in prac¬ 
tice to realize conditions of transmission that ap¬ 
proach ideal ones, to which the Fresnel-Kirchhoff 
theory refers. When appropriate values are taken 
for the reflection coefficient of the ground and the 
four components of the resulting field are added 
vectorially, good agreement has been found between 
experiment and theory for selected terrain. (See 
Chapter 15 of this volume.) Sometimes the terrain 
conditions are often so complicated that they do 
not readily lend themselves to idealization by simple 
geometrical models. For these reasons the Fresnel- 
Kirchhoff diffraction theory has been of only limited 
value in short wave radio propagation. 

A case which quite often can be described ade- 


















































38 


STANDARD PROPAGATION 


quately by an idealized model is that of a sudden 
change of the dielectric properties of the ground, as 
at a coast line. 340 " 346 If the land is rough while the 
sea surface produces full specular reflection, the 
coast line can be considered as a diffracting straight 
edge with respect to the image antenna, rays of which 
represent the field reflected by the sea surface. The 
straight edge serves to cut off that part of the radia¬ 
tion from the image that would represent reflection 
from the land area. The geometrical conditions are 
shown schematically in Figure 8. For the details of 


rays reflected from the sea add to the direct rays, 
and the “lobe” type of pattern appears. It is clear 
that if the diffraction effect were neglected very 
serious errors of the estimated coverage would result. 

Similar methods can be used to treat diffraction 
caused by cliffs, edges of wooded areas, lakes, etc., 
but these cases are not so often of importance in 
radar practice. 

54 THE ELECTROMAGNETIC FIELD 



the analytical treatment the reader is referred to the 
comprehensive report on standard propagation con¬ 
tained in Volume 3 of the Summary Technical Re¬ 
port of the Committee on Propagation. The distor¬ 
tion of the coverage diagram of a radar set caused by 
this type of diffraction is often quite large and be¬ 
comes important operationally at frequencies of 100 
to 200 me. This is illustrated here by a computed 
coverage diagram shown in Figure 9. If diffraction is 



Figure 9. Coverage diagram for coast line diffraction 
(relative field strength). (Heights exaggerated 3.5 to 1.) 


Field Strength Distribution 

If a transmitter is erected over a plane, ideally re¬ 
flecting earth, the well-known lobe pattern results 



Figure 10. Typical coverage diagram (lobes) over 
plane earth. 


(Figure 10), the curves being ones of constant field 
strength. The field is given by 



where hi and h 2 are the transmitter and receiver 
heights, and d the distance from transmitter to 
receiver. The maxima and minima occur at the 
positions in space where 

hM = ~ Xd . (23) 


with n= 1, 3, 5 • • - for the maxima, 
w = 0, 2, 4 • • • for the minima. 

If » hi, the angle of elevation is ^ = hi/d and 
the formula for the maxima and minima can be 
written 


* 


n\ 

4 ~hi ' 


(24) 


not taken into account the coverage pattern shows a 
constant amplitude through higher angular elevations 
reached only by the direct rays since the ground re¬ 
flection is negligible. At lower angular elevations 


If the earth curvature is taken into account the 
pattern remains essentially the same above the line 
of sight, but a number of corrections enter which 
change somewhat the position and strength of the 















THE ELECTROMAGNETIC FIELD 


39 


lobes. The problem is primarily one of geometry, 
taking into account the modification of the direc¬ 
tion, phase, and intensity of the reflected ray caused 
by the earth’s curvature. It can be solved by suit¬ 
able numerical and graphical methods such as are 
given in Volume 3 where the details are extensively 
treated. It may suffice here to enumerate the main 
modifying factors. 

If a tangent to the earth is drawn at the point of 
reflection (Figure 11), the distances h\ and h\ of 
transmitter and receiver from this line are the equiv- 


RECEIVER 



Figure 11 . Geometry over spherica earth. 


alent heights in terms of which the problem is a 
plane-earth problem for that particular ray. They are 
smaller than the heights above the ground hi and 
h 2 , but clearly they are functions of the angle of 
elevation. Thus a set of implicit equations has to be 
solved for each angle of elevation giving h\ and h\ 
as functions of hi, h 2 , and d, whereupon the inter¬ 
ference between the direct and reflected rays is 
computed as in the case of a plane earth. 

In addition to the modification of direction and 
phase at reflection, there is also a change in intensity 
of the reflected ray caused by the fact that the 
reflecting surface is curved. This modification is 
taken into account by the divergence factor, a purely 
geometrical quantity which is part of the reflection 
coefficient, reducing the intensity of the reflected 
ray. 

The behavior of the field below the line of sight 
requires a more powerful line of attack. The line of 
sight itself is given by a tangent to the earth’s surface 
passing through the transmitter. The distance from 
the transmitter to the horizon, when a modified 
earth’s radius ha is used is 


When k — %, hi is in meters and d T in kilometers, 
this becomes 

d T = 4.12 Vhi. (26) 

The diffraction region actually extends at least from 
the lower surface of the first lobe downward to the 
earth’s surface. In the diffraction region well below T 
the line of sight, the field strength decreases very 
rapidly and very nearly exponentially with the 
distance. 

Figure 12 shows a typical example for the ground 



_^ d IN KILOMETERS 

Figure 12 . Field strength versus distance for fixed 
height, vertical polarization. 

constants indicated. The ordinate is the ratio of 
field strength to the free space field; the transmitter 
and receiver heights are fixed and d is plotted as 
abscissa. Above the line of sight the typical lobe 
pattern is exhibited. The decrease of the field in 
the diffraction region is the more rapid the shorter 
the wavelength. In the centimeter band this decrease 
is so rapid that for most practical purposes the field 
is nonexistent near the ground at distances exceeding 
the horizon distance by more than a few kilometers. 
Figure 13 shows a similar diagram for fixed distance 
and variable receiver height. 

Modes 

The description of the electromagnetic field above 
the line of sight is adequately given by means of rays 
and their phases as used in optics. This method ob¬ 
viously breaks down in the diffraction region into 
which the rays do not penetrate. For this region a 
solution of the wave equation is required. Many 
distinguished mathematicians have contributed vary¬ 
ing techniques for solving the wave equation. The 


d T = \/2hahi . 


(25) 








































40 


STANDARD PROPAGATION 



200 -180 -160 -140 -120 -100 -80 


D B 

Figure 13. Field strength versus height of receiver for fixed distance relative to radiation field at one meter from 
transmitter. 


theory in its present form as applied to short and 
microwave propagation has been worked out by 
van der Pol and Bremmer 20 for vertical polarization 
and Marian C. Gray for horizontal polarization. 

The results of the theory may be summarized as 
follows. The electromagnetic field can be represented 
as an infinite series of the form 

E = EoVd^ c m e-Ud !/„(*.) V m (h) (27) 


where E 0 is the free space field and c m and £ m are 
complex constants depending upon |the wavelength 
and the electromagnetic ground constants, hi and hz 
are again the heights of the transmitter and receiver 
above the ground, d is the distance between the two; 
U m are the height-gain functions, and e is the base 
of natural logarithms. The formula is symmetrical 
with respect to the interchange of transmitter and re¬ 
ceiver, in agreement with the principle of reciprocitv. 




































































THE ELECTROMAGNETIC FIELD 


41 


Each of the terms which compose the sum (27) 
is called a mode. The coefficients are complex con¬ 
stants with their real parts positive. They represent 
therefore an exponential decrease of the field strength 
with distance. The real part of is the attenuation 
factor of the rath mode expressed in nepers per unit 
distance. The height-gain functions U m are found to 
increase with height above the ground. The increase 
is first slow but eventually becomes exponential and 
remains that way for large heights. 

The real part of the attenuation factor, in¬ 
creases with increasing mode number; hence, if the 
receiver is far enough from the transmitter, all 
modes except the first one become very small and 
the sum in equation (27) reduces to its first term 
which can be computed without much difficulty. 
This applies when the heights hi and h 2 are fairly 
small. The height-gain functions increase with height 
the more rapidly the higher their order, and as one 
approaches the line of sight the number of modes 
that contribute to the field strength becomes large. 
It is true that the series (27) converges everywhere, 


but above the line of sight the number of terms re¬ 
quired for a good approximation is so large that the 
expression is useless for numerical work. Here the 
methods of ray optics become applicable. It is 
usually found that, at a given distance d, the field 
in the lower part of the diffraction zone can be 
computed by using one or a few terms of the series 
(27). At large heights above the line of sight 
the field is determined by the methods of ray 
optics, and the two curves can be joined with a 
good degree of accuracy by graphical means on 
a decibel diagram. This has been done in Figures 
12 and 13. 

The series (27), though simple in external appear¬ 
ance, still proves extremely difficult to evaluate. 
Burrows and Gray, 23 however, have simplified the 
mechanics of evaluation to such a degree that nu¬ 
merical data can be obtained by means of a small 
number of graphs. The detailed procedures employed 
in computing field strength and contour diagrams by 
the method of modes are summarized and collected 
in Volume 3. 



Chapter 6 

ELEMENTARY THEORY OF NONSTANDARD PROPAGATION 


si HISTORICAL 

D uring 1941 and 1942, short and microwave 
radar sets became available in England and 
were installed along the Channel and North Sea 
coast. Very soon it was found that at certain times 
these sets were able to pick up targets such as ships 
and fixed echoes from the French coast which were 
well below the line of sight and which under the 
conditions of standard propagation would have given 
entirely negligible responses. A relationship with 
the weather soon became apparent. In 1942, enough 
had become known to establish most of the correla¬ 
tions between excessive ranges and meteorological 
conditions which have remained fundamental and 
which are based on the picture of refraction in the 
lower atmosphere that is now generally accepted. 

Later on similar effects with radar sets were dis¬ 
covered all over the world. An example in point is 
in the Mediterranean where nonstandard propa¬ 
gation, during certain seasons, is the rule rather 
than the exception. These conditions will be dis¬ 
cussed in more detail in the chapter on radiometeor¬ 
ology. The most extraordinary ranges, perhaps, were 
found in the Indian Ocean where radar sets operat¬ 
ing at frequencies of 200 me were found on occasion 
to record fixed echoes from as far away as 1,500 
miles. The mechanism of this phenomenon is not yet 
fully understood. 

In the Pacific theater extended ranges have also 
been observed; but, on account of the vast territory 
covered, the technical difficulty of all operations, and 
the inadequacy of meteorological coverage, it is 
difficult to evaluate the results systematically. Up 
to the present, reports on the conditions responsible 
for nonstandard propagation have been received 
from many parts of the world which vary widely in 
their characteristic features and dependence upon 
season, weather, time of day, properties of the 
ground, etc. It is possible to lay down certain general 
rules, but on the whole the phenomena are exceed¬ 
ingly complex. 

During 1943 and 1944, a number of systematic 
experiments on nonstandard propagation were car¬ 
ried out by the British and American Services and 
affiliated organizations. Most of these were one-way 


transmission experiments that have a number of 
advantages over radar experiments, but some of the 
latter also were undertaken. Extensive transmission 
experiments were conducted by the British in the 
Irish Sea and the Americans in Massachusetts Bay, 
the state of Washington, southern California, and 
Arizona, and in the West Indian Ocean. 

These experiments will be described in the next 
chapter. Because of the nature of the subject, it will 
be profitable to discuss the theory before the experi¬ 
ments and to give, in this chapter, an outline of our 
present conceptions of the theory of nonstandard 
propagation. 


REFRACTIVE INDEX 


Nonstandard propagation takes place whenever 
the rate of variation of the refractive index in the 
lower atmosphere deviates considerably from the 
“standard” linear slope defined by equation (11), 
Chapter 5. The variation might consist either in a 
deviation from linearity, which is the most common 
case, or in a linear slope in the lowest layers that is 
widely different from the value assumed for the 
standard. The refractive index is a function of tem¬ 
perature, pressure, and the partial pressure of water 
vapor, given by equation (9), Chapter 5. The de¬ 
pendence of the refractive index on pressure leads 
to a regular decrease with height, but the change of 
barometric pressure with the weather produces only 
an insignificant effect on the gradient. The variations 
of refractive index in the lower atmosphere owe their 
existence to stratifications in which the temperature 
and moisture changes rapidly with height. 

In order to express refraction in quantitative 
terms Snell's law for a curved earth is used as given 
by equation (14), Chapter 5: 

nr cos a = n 0 r 0 cos a 0 . (1) 

Now let 

n = 1 + (n — 1) with n — 1 « 1 

r = a (1 + with - « 1 (2) 

\ a) a 


cos a 



with a « 1 


42 


TYPES OF M CURVES 


I 

.1 


43 


where a is the earth’s radius. Similar expressions 
are valid for the quantities having the subscript 0. 
Multiplying out and neglecting quantities that are 
small of the second order, one obtains 

n - no + l (h - ho) = \ (a 2 - a?) . (3) 

It has become customary to introduce the modified 
refractive index M by 

n + - = 1 + M ■ 10-*, (4) 

a 

whereupon Snell’s law assumes the form 

(M — Mo) • 10 —6 = J (a 2 — ao 2 ) . (5) 

This equation indicates how the angle a between a 
ray and the horizontal changes as a function of M 
which, in turn, is a function of the height, both 
explicitly by equation (4) and implicitly because n 
is a function of the height in a stratified atmosphere. 


TYPES OF M CURVES 


An M curve is a diagram in which M as abscissa 
is plotted against the height h as ordinate. Extensive 
experience has led to a classification of M curves 
which is shown in Figure 1. The six types exhibited 



SIMPLE SURFACE 
TRAPPING 



ELEVATED S SHAPE GROUND-BASED S SHAPE 



Figure 1 . Types of M curves. 


comprise all cases that are of practical interest. 
M curves of a more involved structure are rare. In 
all cases it is assumed in accord with experience 
that at sufficiently high elevations the M curves 
become linear and have, or nearly have, the standard 
slope. 


The height at which these variations in refractive 
index occur may vary from a few feet to several 
hundred or even a few thousand feet though they 
are likely to be found at very low elevations in cold 
climates and at higher elevations in warm climates. 
The meteorological conditions which yield these 
curves will be dealt with extensively in Chapter 9, 
and few indications may suffice here. Ordinarily, 
on going aloft the temperature decreases at a slow 
and fairly steady rate. When, instead, the tempera¬ 
ture increases with increasing height, a phenomenon 
known to meteorologists as a temperature inversion, 
equation (9), Chapter 5, shows that n decreases with 
increasing height. This does not necessarily imply 
that M decreases with height since, by equation (4), 
M contains the term h/a, which increases with 
height. If, however, the variation of temperature is 
sufficiently great, a decrease or inversion of M 
results. Such an inversion produces a duct, a term 
which refers essentially ’to certain meteorological 
phenomena and whose exact significance is explained 
below. A variation of humidity over the layer has 
an effect essentially analogous to, but distinctly 
more pronounced than, the effect of temperature. 
In this case M increases with height with a decreas¬ 
ing moisture content and vice versa. Variations of 
humidity are common in the lower atmosphere, and 
they constitute the main cause of refractive index 
variations, with temperature variations frequently 
a contributing factor. 

The six cases shown in Figure 1 are as follows: 
the standard case which needs no further comment; 
the transitional case where the moisture or tempera¬ 
ture variation is not great enough to produce a true 
inversion of the M curve but merely results in a 
nearly constant value of M in the lowest strata; the 
substandard case in which M increases more rapidly 
with height than in the standard case; and three 
cases of ducts. The simple ground-based duct or sur¬ 
face trapping, consists in an M inversion immediately 
adjacent to the ground or sea. There are two types 
of elevated M inversions distinguished by the posi¬ 
tion of the minimum value of M aloft. If this mini¬ 
mum is larger than the value of M at the ground so 
that the vertical projection from the minimum inter¬ 
sects the M curve, it is considered a true elevated, 
S-shaped duct. If this minimum is less than the 
value of M at the ground it is an elevated M inver¬ 
sion but a ground-based duct. 

In dealing with these M curves it is universally 
assumed that the stratification is the same over the 
















44 


ELEMENTARY THEORY OF NONSTANDARD PROPAGATION 


whole length of the transmission path. This is a 
severe restriction, but it has proved indispensable 
up to date in order to make the problem susceptible 
to mathematical treatment, and it is reasonably often 
fulfilled in practice. 

64 RAY TRACING 

In order to understand the mechanism of trans¬ 
mission of radiant energy in a duct the course of 
rays issuing from the transmitter is traced according 
to equation (5). Note that for the small angles with 
the horizontal at which these phenomena occur, 


where x designates the horizontal distance. Hence 
from equation (5) 

X = J^= Jdh[a 0 2 + 2 (M - Mo) ■ 10— 6 ]—i . (7) 

Since M is a given function of height, equation (7) 
gives in integral form the relation between distance 
and height, where a 0 is the angle with the horizontal 
of the ray emitted by transmitter and M 0 is the 
value of M at the transmitter height. 

Practicable graphical methods of ray tracing have 
been developed and used extensively to compute 
actual coverage diagrams. 66,68 ’ 69,71,76 ' 82 ' 98,99 Three 
schematic pictures of ray tracing, showing the main 
phenomena of interest, are presented in Figures 2, 


upward curvature of the rays. On the left-hand side 
of each diagram the M curve is plotted. By equation 
(5) we have 

a = 0 , 

if 

M = M o - J <* 0 2 • 10 6 . (8) 

The vertical lines drawn on the M curve diagram 
are the values of M 0 — \ a 0 2 • 10 6 for the rays 
selected. Wherever this line intersects the M curve 
the corresponding rays become horizontal and there¬ 
after reverse the sign of dh/dx. In the case of Figure 
3 these reversals combine with reflections from the 
ground to make a family of rays oscillate between 
an upper limit, different for each ray, and the ground. 
The limiting angle of emergence beyond which re¬ 
versal no longer occurs is designated by (2 or 2') 
in Figures 3 and 4. The duct is the vertical interval 
cut out by the intersection of the vertical line desig¬ 
nated by 2 with the M curve or with the ground. 
The terms trapping, superrefraction, or guided pro¬ 
pagation are often employed to describe these phe¬ 
nomena. 

A word might be said here about the substandard 
case which, although much less frequent than the 
duct, is of operational significance. It is readily seen 
that in this case the rays undergo a strong upward 
curvature in the layer in which there is a substandard 
slope of the M curve. As a result of this the apparent 
horizon distance is reduced, and the ranges of radar 
and radio equipment for targets or receivers near 
the ground are greatly diminished. M curves of the 



3, and 4. These figures are plane earth diagrams in substandard type occur often when fog is present but 

which the ordinary downward curvature of the earth are not uniquely correlated with fog. 

has been eliminated and replaced by an additional In order to compute coverage diagrams on this 

















RAY TRACING 


T 


45 




basis it is necessary to know the phases associated 
with the rays so as to determine their mutual inter¬ 
ference. If this is done by an appropriate graphical 
or numerical method, contours of constant field 
strength can be drawn. Figure 5 shows, typical cov¬ 
erage diagrams computed in this way, 146 correspond¬ 
ing to a value of hi/\ = 20. The lines separating 
the “detection zones” from the “blind zones” indi¬ 
cate ranges at which a medium bomber would just 
become visible to the particular radar to which these 
diagrams apply. Diagram 1 shows the undistorted 
lobe diagram for standard refraction while dia¬ 
grams 2, 3, 4, 5 show the coverage diagram for 


various types of ground-based and elevated ducts. 

In Figure 6 is shown the variation of field strength 
with height for various distances for the M curve 
shown on the left-hand side of the figure. 73 The 
transmitter is at a height of 60 m. 

In all diagrams shown in this section the vertical 
scale is vastly exaggerated as compared to the 
horizontal scale. It may readily be shown that when 
the representation is such that the earth is curved, 
the contours of constant height can be represented 
by parabolas in the approximation where the true 
vertical elevations are small compared to the hori¬ 
zontal distances involved. 




























46 


ELEMENTARY THEORY OF NONSTANDARD PROPAGATION 


ALTITUDE IN FEET 



65 GENERAL CHARACTERISTICS 
OF DUCTS 

It is evident that the number of types of M curves 
that one can construct a priori is almost unlimited. 
In practice both the types actually occurring and 
their variability within each type of classification 


are severely limited by meteorological conditions. 

M, as defined by equation (4), is the sum of two 
parts, the true refractive part (n — 1) and the earth 
curvature part h/a. At higher elevations the absolute 
moisture in the atmosphere decreases, and irregular 
variations of temperature become more and more 
exceptional so that eventually, at a relatively great 
height, any M curve approaches the standard curve. 
An additional limitation comes from the fact that 
both the temperature and moisture variations in any 
one climate are subject to definite limitations. An 
extreme moisture change occurs when there is a 
boundary separating a nearly or fully saturated 
warm air mass from a very dry cool air mass. Tem¬ 
perature inversions involving differences of more 
than 10 to 15° C are quite exceptional. As a conse¬ 
quence of this both the actual height of the M 
inversion as well as the difference AM between the 
maximum of M at the bottom and the minimum at 
the top of the M inversion are limited. The height of 
the M inversion layer may be only a few feet if it is 
close to the ground or sea surface. It frequently is 
of the order of 50 to 100 ft or even larger. Under 
particularly favorable conditions in warm climates, 
elevated M inversions may have heights of several 
thousand feet. The duct itself can be appreciably 
thicker than the M inversion layer, as may be seen 
from the structure of the last two M curves in 
Figure 1. 

Again, the decrease AM over the height of the in¬ 
version is limited for the same reasons. For low 
ducts values of the order of AM = 5 to 10 are com¬ 
mon. Somewhat larger values will sometimes occur. 
The maximum value observed is about AM = 40 in 
high-level inversions at San Diego which originate 
in the singular climatic conditions found there. 

An important consideration for the detailed mathe¬ 
matical treatment of duct propagation is the shape 
of the knees of the M curve. This, again, depends on 
the physical nature of the atmospheric stratification. 
Very often the inflections are so sharp that a succes¬ 
sion of two or three straight lines furnishes an excel¬ 
lent approximation. These are known as bilinear and 
trilinear ducts and are of very common occurrence, 
especially with elevated ducts and a large class of 
ground-based ducts. On the other hand, there are 
also ground-based ducts in which the corners are 
extremely well rounded. 

It follows from the restrictions on the numerical 
values of M that there are severe limitations on the 
angle a for which duct effects can occur. Thus AM — 




























































SURVEY OF WAVEGUIDE THEORY 


i 


47 



Figure 6 . Variation of field strength with height for various distances. 


10 represents a change of one part in 10 5 in the re¬ 
fractive index. Now from equation (5), we have 
by differentiation 

AM • 10 6 = aAa . (9) 

For a complete reversal of a ray we must have 
Aa ^ a, and then a is proportional to the square root 
of AM. In the above case, where AM = 10, we find 
that a is of the order of 3 • 1CT 3 , or about 10 minutes 
of arc. 

Carrying considerations of this type into a little 
more detail it is found that the major effects of 
nonstandard refraction occur only for rays which 
emerge from the transmitter at an angle of less than 
Yz degree. For angles between Yi and 1J^ degrees 
the refractive effects produced by the typical non¬ 
standard M curves consist merely in minor modifica¬ 
tions of the standard coverage pattern, while for 
angles above V/i degrees the refractive effects are 
negligible. 

66 SURVEY OF WAVEGUIDE THEORY 

The ray tracing method presented in Section 6.4 
is only a rather rough approximation to the true 
solution of the wave equation. It neglects diffraction, 
which on closer investigation is found to be very 
important. In order to visualize this, the waveguide 
analogue was introduced at an early stage of the 
development. Consider a two-dimensional wave¬ 


guide consisting, for instance, of two parallel plane 
sheets of copper of infinite extent. The propagation 
of an electromagnetic wave in such a guide is some¬ 
what analogous to that in a duct. The reversal 
of the vertical component of the rays by refraction 
in the duct corresponds to the reflection by the walls 
in the case of a metallic waveguide. It is well known 
that wave propagation under these conditions can 
be described by the methods of geometrical optics 
only to a very rough approximation. Soon after the 
discovery of ducts the accurate theoretical treatment 
of duct propagation was initiated in England. 67 ' 70 ’ 71 ’ 
73,88,94 xhe general result of these investigations 
may be summarized as follows. For an atmosphere of 
arbitrary stratification the field can be formally ex¬ 
pressed by the series development, equation (27) of 
Chapter 5. The constants appearing therein and 
the height-gain functions involved are, however, 
different from the standard case and depend on the 
particular M curve involved. The solution, therefore, 
consists again of a superposition of “modes” which 
decay exponentially with distance from the trans¬ 
mitter. The height-gain functions do not, in general, 
increase with altitude all the way up from the ground. 
In the case of a duct the height-gain functions of 
the lowest modes have a pronounced maximum in 
the duct, similar to the curves for the overall field 
strength shown in Figure 6. This maximum becomes 
flatter and eventually disappears entirely for the 
height-gain functions of the higher modes. 

It is useful to supplement the rather complex 
















48 


ELEMENTARY THEORY OF NONSTANDARD PROPAGATION 


mathematical development into modes, represented 
by equation (27) of Chapter 5, by a simpler type of 
analysis which connects it with the ray picture. For 
the sake of simplicity let the phenomena be two- 
dimensional, confined to the horizontal x direction 
and the vertical z direction. If the wavelength is 
small enough compared to the dimensions of the 
duct, the electromagnetic field at some distance from 
the transmitter may, in any sufficiently small volume 
element, be represented by a plane wave whose wave 
front is perpendicular to the direction of the rays. 
Such a plane wave may be written as 

E = E 0 e iwt e~ j{kx+lz) . (10) 

Confining ourselves for the moment to the case of 
the plane earth, it is found from electromagnetic 
theory that 

fc 2 + i* = (^p) , (ii) 


where n is the refractive index in the volume element 
considered, and X is the free space wavelength. Since 
k and l are proportional to the directional cosines 
between the direction of the ray and the x and z axes, 
we may put 


k = 


2 Ten 

—— cos a , 

A 


l 


2tt n . 

—— sin a 

A 


( 12 ) 


where a is the angle between the ray, or the normal 
to the wave, and the horizontal. 

The further mathematical analysis shows that, 
for a horizontally stratified medium where n is a 
function of z only, we have k = constant. In view of 
equation (12) this gives us n cos a — constant, 
which is just Snell’s law for a plane earth, as enunci¬ 
ated before. 

The ray picture, being a rough approximation, 
gives an electromagnetic field in some regions and 
none in others. In the rigorous solution of the wave 
equation there is some electromagnetic field strength 
everywhere. Consider in particular the region just 
above a duct. There are regions of “shadow” above 
the duct caused by the fact that some of the rays 
are bent downward in the duct. Clearly, at the point 
of reversal of a ray, a = 0 and hence l =0. If we 
proceed farther upward in a duct n decreases, and 
it follows from equation (11) that if n decreases 
sufficiently l must eventually become imaginary. 
Instead of a wave component in the z direction we 
then have an electromagnetic field which decreases 


exponentially as we go upwards. In the top layer 
of a duct, the decay takes place very gradually 
because the change in refractive index is extremely 
slow. Eventually, however, n must begin to increase 
again as we go still farther upwards from the duct 
and there comes a height where l is again real and 
an ordinary wave is again possible. This behavior 
might be likened to that of a metal foil so thin as 
to be partly transparent for the waves considered. 
The duct thus may be likened to a waveguide 
bounded on one side by a solid reflector, the ground, 
and on the other by a semi-transparent reflector. 
The mathematical theory of ducts has therefore 
often been designated as leaky waveguide theory. 

A closer study of the height-gain functions which 
appear in the mode formula, equation (27) of Chap¬ 
ter 5, shows that in the presence of a duct the leak¬ 
age across the upper boundary of the latter is the 
more pronounced the higher the order of the mode, 
and that for sufficiently high modes there is almost 
no confinement of the electromagnetic field within 
the region of the duct. In consequence of this fact 
the exponential damping with horizontal distance, 
which is characteristic of each mode, is more pro¬ 
nounced for the higher modes, because for these 
modes the electromagnetic energy rapidly “leaks 
away” from the duct. At large distances from the 
transmitter the field in and near the duct is therefore 
described by the lowest mode alone. This depends, 
of course, partially on the relative strength of excita¬ 
tion as well as on the attenuation of the various 
modes. 

Another aspect of the wave theory of ducts which 
is of great practical importance is the cutoff effect. 
It is well known that any ordinary metallic wave¬ 
guide has a cutoff frequency below which the guide 
cannot transmit an electromagnetic wave. The mathe¬ 
matical treatment of the duct shows that there is 
a similar lower limit of frequency for transmission 
through a duct, but, because of the “leakage” 
phenomenon, it is found that there is no sharply 
defined cutoff frequency but a gradual decrease of 
the duct’s ability to confine radiation within itself 
with decreasing frequency. Figure 7 is a graph 
giving representative values for what may be taken 
as the cutoff frequency of a duct as a function of its 
height in feet and AM, the decrease of M in the in¬ 
version layer. These values are the result of a some¬ 
what crude approximation and should not be taken 
to indicate more than the order of magnitude of the 
frequency at which this effect occurs. 



REFLECTION FROM ELEVATED LAYERS 


49 



Figure 7. Maximum wavelength trapped in a simple 
surface duct. Duct width d in feet. A M is total decrease 
of M in duct. X max = 2.5 d V A M 10- 6 . 


67 REFLECTION FROM ELEVATED LAYERS 

Reflection from elevated layers has so far been 
observed systematically only under the rather spe¬ 
cial meteorological conditions at San Diego, but it 
probably occurs elsewhere, though with a lesser 
degree of regularity. It appears when there is a 
strong elevated M inversion. Such an M curve is 
very nearly equivalent to a true discontinuity of 
refractive index, and the effect on a wave traversing 
such a region is similar to that of a boundary between 
two media, the more nearly so, the larger the M- 
inversion gradient. If there is a true discontinuity, 
an incident wave is split up into a reflected and a 
transmitted wave. If the discontinuity is replaced 
by an M inversion layer, the reflected wave still 
persists but becomes weaker the less steep the in¬ 
version. The distinction between this phenomenon 
and the apparent reflection in the duct where the 


rays become horizontal before turning downward is 
usually fairly cle&r-cut. The true reflection described 
here occurs primarily in waves which are so long as 
to be below the cutoff. 

There exists a case of gradual transition between 
two media with different refractive indices for which 
the wave equation can be integrated. 444,445 

This can be applied qualitatively to the case, 77 ’ 91 
in so far as earth’s curvature can be neglected. 
Figure 8 shows the calculated ratio in decibels of 



reflected to incident wave for various angles of in¬ 
cidence plotted against the ratio of thickness of the 
transition layer to wavelength as abscissa. 

The verification of this theoretical concept in the 
San Diego experiments will be discussed in the next 
chapter. 











































































Chapter 7 

METEOROLOGICAL MEASUREMENTS 


7.i INTRODUCTION 

T he direct measurement of the refractive index 
of air is carried out in the laboratory under 
closely controlled conditions. The variations of the 
refractive index in the atmosphere which are of 
paramount importance for propagation problems are 
determined indirectly by measurements of the tem¬ 
perature and humidity. From the values of these 
latter the refractive index is computed by equation 
(9) of Chapter 5. There has been no reason, so far, 
to doubt the reliability of this procedure, and specu¬ 
lative assumptions of the failure of this relation 
which have been brought forward at times during 
the war have not been accepted. 

This chapter describes measuring equipment that 
was especially developed during 1943 to 1945 to 
study refractive index variations. Following this 
description is a collection of actual M curves which 
have been measured in different parts of the world 


72 TEMPERATURE AND HUMIDITY 
ELEMENTS 

The value of the refractive index n, or of M as 
defined by equation (4), Chapter 6, is sensitive to 
relatively small changes in temperature and especially 
in humidity. Both accuracy and speed in determina¬ 
tion of M are required. Speed is especially necessary 
because a considerable number of points generally 
are needed to determine the shape of an M curve. 
Electrical methods have been used almost exclusively 
for these measurements, though an ordinary psychro- 
meter will do in the absence of more specialized 
equipment. 

There is no particular difficulty in measuring the 
temperature with suitable accuracy, such as ±0.2 C. 
The electric resistance element used in the Bureau 
of Standards radiosonde is well suited to the purpose 
and is commercially available. More recently ther¬ 
mistors have been used. At stationary installations 
in England ordinary nickel or platinum resistance 
thermometers have been installed, primarily for 
recording purposes. 


Humidity may be measured either directly, or 
indirectly by measuring the wet bulb temperature. 
Hair hygrometers are unsuitable because of their 
large time lag. For the direct measurement of 
humidity electrolytic resistance elements, such as 
are standard in the U. S. Weather Bureau radiosonde, 
are used. The active agent in this type of element is 
an aqueous solution of lithium chloride which is 
deposited as a film on a small cylinder. The resist¬ 
ance of the solution is highly sensitive to changes in 
relative humidity of the surrounding air. In England 
a variant of this principle has been employed where 
the lithium chloride solution is absorbed in a cotton 
cloth. 

In the indirect method of measuring humidity a 
thermistor of cylindrical form is surrounded by a 
moist wick which, with proper aeration, indicates 
the wet bulb temperature. To insure insulation the 
element is covered with several coats of insulating 
lacquer before the wick is attached. 

The main problem in all these devices is that of 
time lag. When mobile carriers such as captive 
balloons, kites, airplanes, or ships are employed, it 
is in general necessary to obtain an individual reading 
within less than a minute, and the response of the 
measuring elements to the temperature and humidity 
of the ambient medium must be reasonably close 
within the time available. 

The time lag constant is the time required to 
attain the fraction 1 — (1/e) = 0.63 of the total 
change, if the temperature (or humidity) is changed 
suddenly. For the temperature elements the time 
lag constant is several seconds in an air stream with 
a velocity of 2 to 5 m per sec. The lag depends 
somewhat on the position of the element relative to 
the air stream and is a maximum when the element 
is perpendicular to the stream. The lag constant of 
the same element, used as wet bulb indicator with 
wick applied, is only slightly larger than that of the 
dry element. The lag constant of the Bureau of 
Standards humidity element has been measured in 
several laboratories, and there seems to be some 
controversy as to its exact value, the results varying 
from a few seconds to about 45 sec, 228 the latter in 
an air stream of 2 to 5 m per sec. 238 


50 


THE WIRED SONDE 


51 


73 THE WIRED SONDE 

Temperature and humidity elements of the type 
described are combined in a lightweight assembly 
which can be moved rapidly through the lower 
atmosphere. Such equipment, when first built in 
England, used dry and wet thermopiles , 227 and 
soon thereafter the same method was adopted by 
the State College of Washington , 228,232,234 and, with 
slight modification, by the Navy Radio and Sound 
Laboratory [NRSL] at San Diego . 236-238 This design 
uses a combination of a resistance temperature 
element and an electrolytic humidity element. The 
instrument developed by the Radiation Laboratory 
of the Massachusetts Institute of Technology uses 
dry and wet resistance elements . 229 

The physical assembly consists of bakelite tubing, 
in which the two elements are mounted perpendicular 
to the axis. The tube is surrounded by a radiation 
shield of aluminum foil. Wet and dry bulb instru¬ 
ments need artificial aeration in calm air which is 
provided by a small electric fan. Among the instru¬ 
ments containing electrolytic humidity strips only 
the late model of NRSL incorporates artificial aera¬ 
tion. Other instruments of this type, when used in 
calm weather with a captive balloon, are aerated by 
giving the cable a few jerks of several feet amplitude. 

In both captive balloon and kite equipment only 
the measuring elements are carried aloft with fine 
wires in the cable to connect with the rest of the 
circuit. The assembly that is carried aloft is therefore 
quite light, weighing only about a pound in the case 
of nonaerated instruments and 3 to 4 pounds for 
aerated ones. 

Figure 1 shows a wiring diagram for the Washington 
State College sonde. The diagram is largely self- 
explanatory. The switches Si S 2 S 3 are contained in 
the pile-up of a single relay and are actuated by a 
miniature worm-geared motor as shown. They reverse 
the current through the elements in order to avoid 
polarization, while at the same time maintaining 
constant polarity at the meters. The period of 
reversal is 0.5 sec and the 1 , 000 -juf condensers in 
parallel with the meters serve to smooth the inter¬ 
rupted current. 

Figure 2 shows a schematic wiring diagram for the 
dry and wet bulb resistance elements of the Radiation 
Laboratory instrument. The resistance of the thermal 
element X controls the bias of one triode of the 
double triode 6SN7 which acts as a vacuum tube 



Figure 1 . Circuit diagram for State College of Wash¬ 
ington wired sonde. 



Figure 2. Circuit diagram for electronic amplifier for 
measuring temperature. (Radiation Laboratory, MIT.) 


voltmeter to compare the resistance of the thermal 
element with a standard resistance. A 1 -ma recording 
meter is placed between the two plates. In operation 
the dry and wet elements are switched into the 
circuit alternately. Calibration of the amplifier is 
obtained by switching a series of precision resistors 
in steps of 1,000 ohms into the circuit in place of the 
thermal element. The stability of this voltmeter is 
such that with a change in line voltage between 95 
and 120 v there is no observable change of the 
meter at any given deflection. 



































52 


METEOROLOGICAL MEASUREMENTS 


7.4 REFRACTIVE index measurements 

The methods which have been used to make 
refractive index measurements in the lower atmos¬ 
phere are the following: 

1. Stationary installations on towers, usually with 
automatic recording on the ground. Aerated wet and 
dry bulb instruments are installed at several heights 
giving a continuous survey of the M curve between 
the ground and the top of the tower. 

2. Installations similar to (1), on shipboard, with 
the meters or recording equipment in the ship’s 
cabin. In order to explore the humidity distribution 
in the lowest layers adjacent to the sea surface, the 
instruments have been mounted at the end of a beam 
that pivots about a horizontal axis fastened to the 
side of the ship. This device has been used extensively 
in the Irish Sea experiments. Artificial aeration of 
shipborne installations is not usually necessary 
because in calm weather the necessary velocity of 
the air is provided by the motion of the ship. 

3. Airborne installations. The unit is mounted at 
a convenient place on the outside of the plane where 
it is not affected by motor exhaust or propeller slip 
stream, with the meters or recorders in the ship’s 
cabin. Comparatively slow-flying planes have been 
used for such measurements, not only in order to 
minimize the dynamic temperature correction, but 
also because in a fast-flying plane too long a column 
of air will be sampled during the period of relaxation 
of the instrument. In airplane measurements it is 
necessary to keep track of the altitude of the plane 
by means of a carefully calibrated altimeter. 

4. Captive balloons and kites. In these devices only 
the measuring unit is carried aloft, the indicating or 
recording meters remaining at the ground. Three 
wires are required when the instrument is nonaerated 
and two additional ones when an aeration motor is 
provided. The wires are of thin insulated copper, 
stranded together into a cable, although more 
recently aluminum wires have been tried because of 
their greater mechanical strength. 233 The fine wires 
of the cable are wound in a high-pitch spiral around 
a strength member consisting of fishline and then 
glued to the latter. Considerable effort has been spent 
on the development of these cables which constitute 
the most critical part of the balloon sonde equip¬ 
ment. For details the reader is referred to the reports 
listed under Meteorological Equipment in the Bib¬ 
liography (Report WPG-14). 

Captive balloons are used in calm weather and in 


winds not exceeding about 4 m per sec. For higher 
wind velocities the balloons become difficult to mani¬ 
pulate, and a kite is then used to carry the measuring 
unit aloft from the ground or even from shipboard. 
Small barrage balloons have a greater lift than 
ordinary weather balloons and can be used in the 
same winds as kites because of their streamline 
shape. They are, however, less mobile and require 
more hydrogen than the smaller balloons. 

The cable for the balloon or kite is wound on a 
drum, and connection with the stationary meters is 
made by means of slip rings. The height of the balloon 
or kite is determined by the length of cable paid out 
together with a rough measurement of the angle 
of the cable. 

•Captive balloons reach heights of several hundred 
feet without difficulty and even heights of 1,000 to 
2,000 ft are not infrequent. 


75 OTHER METEOROLOGICAL 

INSTRUMENTS 

It is hardly necessary to say that measurements 
of atmospheric temperature and humidity are pos¬ 
sible and have been made, with instruments of a 
more conventional type. In the early stages of our 
knowledge of nonstandard propagation, surveys were 



O IO 20 30 40 50 60 


M-M 0 

Figure 3. Representative standard M curve. (36 M 
units per 1,000 ft.) 

made by means of an ordinary psychrometer held 
out of the window of a slowly cruising plane and 
aerated by the slip stream. The British installations 

































HEIGHT, FEET 


OTHER METEOROLOGICAL INSTRUMENTS 


53 



-20 -10 0 10 
M-M 0 



•20 -10 0 10 20 



0 10 20 30 40 


M-M 0 


M-M 0 


Figure 4. Representative nonstandard M curves from the Massachusetts coast. 



Figure 5. M curves from the Massachusetts coast showing strong ducts. 



Figure 6. M curves from New Zealand, east coast near Cook Strait. 



































































































































































FEET 


54 


METEOROLOGICAL MEASUREMENTS 



Figure 7. M curves from a flight west of San Diego. 















REPRESENTATIVE OBSERVED M CURVES 


55 



Figure 8 . M curves from Taboga Island near Balboa, Canal Zone. 


commonly use multi junction dry and wet thermo¬ 
piles which have the advantage of not requiring 
elaborate calibration. In connection with captive 
balloons this type of equipment is somewhat clumsy 
in that the cold junctions have to be carried aloft 
in a Dewar flask. 

It should be noted here that the ordinary 
noncaptive radiosonde as used in the routine meteoro¬ 
logical observations of the U. S. Weather Bureau and 
of the Armed Services is not suitable for radio- 
meteorological purposes. The reason is that these 
sondes are designed to give representative data only 
at definite and fairly large vertical intervals, 100 ft 
or more. These are too widely spaced to yield a 
representative M curve, as the characteristic features 
of the latter are usually concentrated in the lowest 
strata of the atmosphere. 

Wind measurements are of importance in connec¬ 
tion with propagation problems, for reasons which 
will be given in detail in the chapter on weather 


forecasting. They are particularly significant at 
coasts when off-shore winds or land and sea breezes 
are present. Sensitive and carefully calibrated 
anemometers with ordinary wind vanes prove 
adequate for measurements of this type. Special 
equipment such as supersensitive anemometers, 
developed for particular purposes such as chemical 
warfare problems, are not usually needed because 
the large area covered by radio transmission paths 
or radars renders too detailed measurements useless. 


76 REPRESENTATIVE OBSERVED 
M CURVES 

A small catalogue of M curves that have been 
actually measured in various parts of the world by 
means of the equipment described previously con¬ 
cludes this chapter. Most of the curves presented 
were taken over the ocean merely because the 


























































56 


METEOROLOGICAL MEASUREMENTS 



370 380 390 380 390 400 410 

M 

Figure 9. M curves from the New Guinea area. 


majority of experimental measurements have been 
made there. Experience indicates that there is not 
much difference in the types of M curves over land 
and over sea except that standard propagation con¬ 
ditions will in general be much more common over 
land for reasons that will appear in Chapter 9. In 
all these graphs the actually measured points are 
entered so that the reader may gain an idea of the 
degree of accuracy obtained with this equipment. 

Figure 3 shows a standard curve as measured at 
the coast of Massachusetts. The linearity of the 
refractive index in this case is not an accident but 
is the result of the definite physical condition of 
thorough turbulent mixing in the lower atmosphere, 
as will be explained in more detail in Chapter 9. 
Since this is a fairly frequent condition, standard 
curves are actually quite common, and in them the 
measured points cluster well around a straight line 
as shown in Figure 3. 

Figures 4 and 5 show a set of nonstandard curves 
selected from a large series of measurements taken 
on the Massachusetts coast in the summer and fall 
of 1943. 210 Here the M curves are quite irregular, 
perhaps more so than is common at other locations. 
These curves show various types of ducts, some of 
them rather weak, others with a decrease of M as 
much as 20 units or even more. 

Figure 6 is a set of M curves that were measured 
on the east coast of New Zealand, at a point some 
100 miles south of Cook Strait. 223 These curves 
provide good examples of the type of M curves that 
consist of several very nearly linear sections. 

Figure 7 illustrates the typical elevated duct found 
in the San Diego region. Both below and above the 
inversion region the M curve is standard. The various 
curves shown were measured at several distances on 
a flight from San Diego outward. 



382 384 386 388 

M 


Figure 10. Detailed M curve taken over the ocean near 

New Guinea. 

The curves of Figure 8 were taken at Taboga 
Island, some 15 miles south of Balboa, at the eastern 
entrance to the Panama Canal. They show various 
familiar types of ducts; two of the curves represent 
transitional cases where the M curve is steeper than 
standard but does not bend backward. 

Figure 9 shows two soundings from the tropical 
Western Pacific. The curve at the left was taken at 
Biak Island, New Guinea, and is remarkable for the 
presence of two ducts, a ground-based and an 
elevated one. The curve at the right was taken 
at Saipan. 

Figure 10, taken near New Guinea, shows in more 







































REPRESENTATIVE OBSERVED AI CURVES 


57 



M 

Figure 11. M curves over the ocean at Antigua, British West Indies. 


detail the structure of the low maritime duct which 
in this case is only about 30 ft high. 225 This type of 
duct has been studied carefully in the transmission 


experiments at Antigua in the West Indies which 
are reported in Chapter 8. Two typical soundings 
taken near Antigua are reproduced in Figure ll. 194 























Chapter 8 

TRANSMISSION EXPERIMENTS 


8.i BRITISH EXPERIMENTS 

I n the development of short and microwave 
communication and radar, the British were first 
to make systematic transmission experiments on a 
large scale. A number of such experiments were 
carried out at wavelengths below 50 cm, beginning 
about 1936 with some transmission paths over land, 
some over sea; and experiments in the 10-cm band 
were undertaken in the early years of the war. These 
experiments will not be reported individually because 
the earlier results are reproduced and verified in the 
later and more elaborate trials. Instead, attention 
will be confined to two major experiments, one over 
the sea and one over land. 3,10 

The Irish Sea Experiment 

This transmission experiment represents a 
cooperative enterprise undertaken jointly by the 
Radio Division of the National Physical Laboratory, 
the Telecommunications Research Establishment, 
Signal Research and Development Establishment, 
The Ministry of Supply, The Naval Meteorological 
Service, The Meteorological Office, and the General 
Electric Company, Ltd. One-way transmission with 
stationary apparatus was carried on in the winter 
of 1943 to 1944 and continued in operation until 
the end of the war. 

Practically all the transmission is over the sea at 
wavelengths of about 9, 6, and 3 cm. At each fre¬ 
quency the transmitted signal consists of square 
pulses, with equal on-off periods and a repetition 
frequency of 1,000. The 1,000 cycle component of the 
modulation is rectified in the receivers to operate 
the recording milliammeters, and provision is made 
for monitoring the transmitter power and the sensi¬ 
tivity of the receivers in terms of a suitable standard. 
Parabolic mirrors 48 in. in diameter are used for all 
transmitters and receivers and are permanently 
mounted inside the station buildings behind large 
canvas-covered “windows.” 

There are two transmission paths, 57 and 200 
miles in length, which run roughly from south to 
north, but diverge from each other by about 17 
degrees and have the transmitting station in common 


at the southern tip in South Wales. There are trans¬ 
mitting stations A and B at 540 and 90 ft above sea 
level respectively. The receivers, C and D, for the 
short path are in North Wales at two heights, and 
E and F, for the long path, in Scotland at two heights. 
In units of the geometrical horizon distance the 
lengths of the various transmission paths are as 
follows. 

AC BC AD BD AE AF BE BF 

0.89 1.21 1.40 2.40 3.82 4.92 5.63 8.45 

It has not been found possible to utilize all these 
paths at the same time, because the amount of 
records accumulated proved too great for evaluation, 
but selected runs at various frequencies and for 
several paths have been made. 

There is an elaborate setup for measuring meteoro¬ 
logical conditions simultaneously with the intensity 
of the transmitted signal. A weather station is 
located at each of the three terminals, but the main 
meteorological program is carried out from ships 
which ply along the transmission paths. The Admiralty 
has detailed three ships for the sole purpose of making 
these measurements so that the transmission path is 
continuously covered by at least one ship on duty. 
The ships are provided with elaborate meteorological 
equipment of the type described in Chapter 7. 

Results 

The following is a qualitative summary of some 
of the results obtained thus far. 

1. There is general agreement between signal 
variations over the two paths, though the short 
period variations often differ. 

2. Signals are obtained over the long path only 
when the signal strength over the short path BD is 
high. But if the latter condition is fulfilled, the former 
does not always follow. 

3. There is a marked diurnal variation when the 
general signal level is low or moderate with strong 
signals in the late afternoon or evening and a 
minimum between 6 a.m. and 9 a.m. 

4. There is evidence of an appreciable seasonal 
variation with high level for a greater fraction of 
the time in summer than in winter or spring. 



BRITISH EXPERIMENTS 


59 


5. Low level occurs commonly, but not always in 
conditions of fog or low visibility. 

6. Low signal level is usually observed at the 
passage of warm fronts and high level at the passage 
of cold fronts. 

7. Generally speaking, high signal level tends to 
occur in periods of anticyclonic weather. 

A typical record of signal strength for 9-cm waves, 
representing hourly mean values for a month, is 
shown in Figure 1. These records are from two 


Hatch and the /General Electric Laboratories at 
Wembley. The wavelength is in the 10-cm band, 
and transmission, monitoring, frequency control, and 
recording are fully automatic. The path is optical 
except for some houses and trees near the receiver 
which introduce a diffraction loss estimated at 30 
db. As is generally the case with paths that are 
optical or nearly so, the fluctuations of received 
intensity are far less than in the case of long non- 
optical paths. Figure 2 shows a record for one month 



Figure 1. Signal strength in decibels above 1 /jlv receiver input. S band hourly means, June 1944. (Irish Sea experiment.) 
(C = cold front, W = warm front, O = occluded front.) 


links of the short path, both nonoptical. Important 
meteorological phenomena, especially passage of 
fronts, are shown at the top of the diagram. W indi¬ 
cates warm, C cold, 0 occluded. Note in particular 
the standard and the free space level indicated on 
the lower record and the free space level on the 
upper. The standard level for the latter would be 
about 33 db below the zero line. This record, which 
is by no means exceptional, gives a fair idea of how 
vastly the signal exceeds the magnitude calculated 
for standard conditions. At the same time it shows 
the highly irregular character of these phenomena 
and the difficulty of correlating them in a simple 
way with the weather or other conditions. 


2,3,45 ,6 , 7 , Q ,9 , 10 , 11 , 12 , 13 , 14 , 15 




I ' 2 ‘ 3 ‘ 4 1 5 6' 7 0 '9 ' 10 ' II ' 12 ' 13 ’ 14 ' 15 


a 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , , 

5 A, A . h P 

26 , 27 ,28 ,29 ,30 

[30 

/v A aJ Ar 

f\ 

~ f\ 1 L K y\ N 

20 



V 1 






10 

3 16 ' 17 1 18 1 19 '20 ' 21 ' 22'23 '24 ' 25 ' 26 

V 

27 '28 '29 ' 30 



Figure 2. Whitwell Hatch-Wembley path, March 1944. 
S band hourly mean intensities in decibels above 1 /iv 
receiver input. 


Overland Path 

An experimental overland path 38 miles has long 
been operated in the neighborhood of London between 
the Admiralty Signal Establishment at Whitwell 


in 1944. The large diurnal fluctuations in amplitude 
with maxima above normal in the early morning 
hours occur in the beginning of the month and at 
several occasions later, especially from the 21st to 
the 26th. These are related to weather conditions 













































































































60 


TRANSMISSION EXPERIMENTS 


with clear skies, as will be explained in Chapter 9. 

The work undertaken in England on experimental 
transmission paths of various types is quite extensive, 
and the preceding description hardly gives an idea 
of the variety of experiments made and results 
obtained. Most of the experiments are of a smaller 
size than the ones described here. 

82 EXPERIMENTS AT THE EASTERN 
COAST OF THE U. S. 

In the early years of the war a transmission 
experiment was undertaken by RCA Communica¬ 
tions, Inc., between New York and two points on 
Long Island. 131,155 The short path of 42 miles was 
optical, but the long path of 70 miles was nonoptical, 
the receiver being about 400 ft below the trans¬ 
mitter’s line of sight calculated on a % earth’s radius 
basis. Transmission was carried out on 45, 475, and 
2,800 me. The results show what has been confirmed 
by later experiments, that the amplitude of fluctua¬ 
tions is larger the higher the frequency. On the 
optical path the range of fluctuations of the 45-mc 
signal averages only +3 db, whereas over the same 
path the 475-mc and 2,800-mc signals exhibited 
fluctuations which were in excess of 40 db, so far as 
they could be measured. As was to be expected, the 
2,800-mc signal fluctuated more than the 475-mc 
one. Over the nonoptical path all three signals show 
very wide fluctuations of intensity, the rate and 
amount again increasing with the frequency. 

In the course of these experiments a certain amount 
of meteorological study was carried out and fore¬ 
casting of propagation conditions was done on a 
tentative basis. The general results again fore-shad¬ 
owed the more complete data obtained by later 
studies, and a description of the details will be 
omitted here. 

Similar experiments were carried out simultane¬ 
ously by the Bell Telephone Laboratories [BTL] on 
optical paths near New York City. The wavelengths 
employed were 10, 6, and 3 cm. 168,174 Here we find 
clearly established the different signal or fading 
types that are described in detail below. 

A very extensive program of transmission measure¬ 
ments was carried out by the Radiation Laboratory 
of Massachusetts Institute of Technology [MIT]. 
The meteorological records were made in cooperation 
with the U. S. Army Air Forces. The first measure¬ 
ments were made in 1942, and experiments on a very 
large scale were carried out in 1944.3, io, 12 , 153 , i83 t wo 


optical transmission paths were operated in 1943, 
a 22-mile path over the sea and a 45-mile path over 
land. A 10-cm continuous signal was used, and the 
strength was monitored by means of thermistors. The 
antennas were dipoles with 30-in. parabolic reflec¬ 
tors. The received signal was automatically recorded 
on meters having a range of 60 db. The signals 
received were correlated with meteorological observa¬ 
tions, the results of which will be given below. 

In the spring of 1944 a new over-water transmission 
path was installed which was operated simultaneously 
with the 22-mile one. This path was nonoptical, 41 
miles long, and crossed Massachusetts Bay from the 
southern tip of Cape Ann to the northern tip of Cape 
Cod near Provincetown. Transmission over this path 
was carried on with 256-cm waves, 10-cm S band, 
3-cm X band, and 1.25-cm K band. The 256-cm 
equipment used Yagi antennas and operated with 
continuous waves. The microwave transmitters used 
pulses with a repetition frequency of 700 c and used 
parabolic reflectors as antennas. 

The transmitter for the short path was about 120 
ft above mean sea level, and the transmitters for the 
long path were at a similar height. The two receivers 
were about 136 and 30 ft above mean sea level. The 
transmitter power was monitored and continuously 
recorded during the experiments while the receivers 
had automatic frequency control with apparatus 
which searches for the signal if it is lost. The auto¬ 
matic gain control of the receivers was arranged to 
give a spread of the signal over 70 to 80 db. The 
receivers were directly calibrated by means of signal 
generators and a very close check was kept on their 
performance throughout. The rectified output of all 
receivers was fed directly into recording milliammeters. 

Coincident with the operation of these transmission 
paths there was a very extensive meteorological 
program determining sea and air temperatures and 
atmospheric humidities by means of fixed installa¬ 
tions, captive balloons, ships, and airplanes. The 
distribution of the refractive index along the trans¬ 
mission path was thus known in considerable detail 
during practically the whole course of the experi¬ 
ments. Concurrently with these measurements, a 
program of forecasting the transmission conditions 
was carried out. 

Results 

The results obtained on the various transmission 
paths on the east coast of the United States are 



OB BELOW I WATT OB BELOW I WATT DB BELOW I WATT OB BELOW I WATT DB BELOW I WATT 


EXPERIMENTS AT THE EASTERN COAST OF THE U./ S 


61 






Figure 3. Microwave signal types S A and X band, Massachusetts Bay 

















































































































































































































DB BELO# I WATT OB BELOW f WATT DB BELOW I WATT DB BELOW I WATT DB BELOW I WATT 


62 


TRANSMISSION EXPERIMENTS 




Figure 4. Signal types at 256 cm (117 me per sec), Massachusetts Bay, 

































































































































































































































































































EXPERIMENTS AT THE EASTERN COAST OF THE U. ,S. 


63 


rather closely similar to each other, and the graphs 
presented here may be taken as being characteristic 
of all of them. 

Figure 3 shows the signal types observed at the 
microwave frequencies, S band and X band. The 
first type is well above the standard level with high 
signal on the average. It has roller fades with periods 
of from 2 min to an hour or so which may go down 
to the minimum detectable level. These periods are 
generally shorter at any time on the X than on the 
S band. When this type of signal was present on the 
S band, it was almost invariably present on the X 
band and on both the short and long paths. It always 
occurred simultaneously on the high and low receivers 
at any frequency. 

The second type is high and steady at anywhere 
from 5 to 30 db above the standard, generally higher 
on the X than on the S band. Most of the time this 
type occurred simultaneously on both bands, but 
there were some occasions when the S-band signal 
was of the high and steady type while the X one 
was of the first type, high with roller fades. 

The third type of signal is about standard and 
fairly steady which may be a limiting case of the 
high and steady variety. It does not necessarily occur 
on both frequencies and on both high and low 
receivers at the same time. 

The fourth type is standard on the average, with 
scintillations of more than 10 db. The reason for the 
difference between this and the preceding type has 
not yet been established. The scintillations may 
occur on either the S or X band while at the same 
time the other signal is steady. 

The fifth type, known as “blackout,” is far below 
standard and shows strong scintillations. In general 
it occurs simultaneously on both frequencies, both 
paths, and on both high and low receivers. 

Figure 4 shows a similar set of signal types as 
observed with 256-cm waves. These are distinct 
from those observed at the microwave frequencies 
not only in appearance but also in times of occur¬ 
rence. In general no relation has been found to exist 
between the signal type at this frequency and that 
observed simultaneously on S or X band, although 
on rare occasions such a relation is indicated; the 
type may remain constant on one frequency and 
change on the other. Steady signal is most frequent 
at 256 cm, but the other types shown also occur 
fairly often. Variations of 30 to 40 db overall take 
place, and the variations may be fast or slow. 

A statistical study of the frequency of occurrence 


of various signals reveals some rather interesting 
features. Table 1 shows the frequency of occurrence 
of above standard, standard, and below standard 
types on the S and X bands during three typical 
weeks in the summer of 1944. In these statistics the 
range of the standard signal was taken as ±5 db 
for the S band and ±10 db for the X band. The 
behavior of the K-band signal is quite similar to 
that of the other two. 


Table 1 . S and X bands, July and August. 


Date 

Per cent of 
time above 
standard 

Per cent of 
time below 
standard 

Per cent of 
time 
standard 

July 10-16 

63 

36 

1 

Aug. 21-27 

97 

3 

0 

Aug. 28-Sept. 3 

80 

15 

5 


As the season progressed into the fall, standard 
signal became more common and substandard signal 
less frequent especially in the S band. This is shown 
in Table 2. 


Table 2. S and X bands, September and October. 


Date 

Per cent of 
time above 
standard 

Per cent of 
time below 
standard 

Per cent of 
time 
standard 

Sept. 25-Oct. 1 

S 

58 

15 

27 


X 

80 

10 

10 

Oct. 16-22 

s 

76 

2 

22 


X 

92 

0 

8 


These statistical results are characteristic of the 
over-water path near a coast used in the experiments 
of the Radiation Laboratory; and, while the signal 
types shown in Figures 3 and 4 are about the same 
in overland paths, the relative frequency of incidence 
for the various types is quite different. This frequency 
depends not only on the location of the path but, 
also as shown above, on the season. A more detailed 
analysis shows that it also depends on the particular 
weather situation, which may prevail for periods of 
several days or longer. 

It has been mentioned before that the signal 
patterns on the S and X bands and those on the 
high and low receivers are closely parallel. Figures 5 
and 6 show these correlations graphically; the first is 
between the S and X bands and the second is between 
the high and the low S-band receivers. In contradis¬ 
tinction there is practically no correlation between 













64 


TRANSMISSION EXPERIMENTS 


20 


40 


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DB BELOW 1 WATT 
S BAND 


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Figure 5. Correlation between S- and X-band signal 
strengths, Massachusetts Bay. 



DB BELOW 1 WATT 
HIGH RECEIVER 


Figure 6. Correlation between signal strengths at high 
and low receivers, Massachusetts Bay. 



DB BELOW 1 WATT 
S BAND 


Figure 7. Correlation between 117-mc and S-band sig¬ 
nal strengths, Massachusetts Bay. 


the S-band and 117-mc signal levels, as Figure 7 
indicates. 

It is hardly necessary to state that the high signal 
levels occur when the meteorological measurements 
show the presence of a duct and the substandard 
signals occur when the M curve is of the substandard 
type. It will not be possible, in this summary report, 
to enter into the detailed relationship between signal 
strength and M distribution. In a general way the 
experimental results confirm the electromagnetic 
theory in so far as it has been worked out at present. 

Another aspect of the short wave transmission 
that has been studied in these experiments is the 
relationship between radio and radar transmission. 
Since radar involves two-way transmission, its path 
factor, as defined in the beginning of Chapter 5, is 
the square of the path factor for one-way trans¬ 
mission. Therefore the change with distance in the 
received-field strength is more rapid with radar than 
with the one-way radio. 

In order to study this relationship, two small 
mobile radar sets on the S and X bands were set 
up near the transmitter of the long path, at Province- 
town. Echoes from natural targets along the coast 
of the mainland were studied in connection with the 
soundings and correlated with the one-way trans¬ 
mission measurements. In Figure 8 is shown a 
correlation between the signal strength of the X-band 
radar and the signal strength of the high X-band 


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100 80 60 40 

DB BELOW 1 WATT 
SIGNAL STRENGTH 


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Figure 8 . Correlation between one-way and radar sig¬ 
nal strengths over the same path. X band, Massachu¬ 
setts Bay. 







































































EXPERIMENTS IN NORTHWEST 


receiver of the long transmission path. The radar 
target is near the one-way receiver so that both paths 
are practically coincident. When the radar signal was 
below the limit of sensitivity, it is indicated on the 
graph by this limit so that the lower points of the 
diagram really have little physical significance. If a 
straight line is drawn, averaging the variation of the 
higher points, its slope is roughly 2:1 as should be 
expected. 


200 

180 

160 

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60 

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100 80 60 40 

DB BELOW 1 WATT 
SIGNAL STRENGTH 

Figure 9. Correlation between maximum radar ranges 
and one-way signal strength. X band, Massachusetts 
Bay. 

Figure 9 shows a correlation between the one-way 
signal strength on the S band and the maximum 
range of fixed echoes detected by the S-band radar 
along the coast. It is interesting to note that super¬ 
standard radar ranges do not appear until the one¬ 
way signal has reached a certain, rather larger value. 
The one-way signal does not seem to be able to 
increase much beyond this value, whereas the range 
of detectable radar targets rises with extreme rapidity. 


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65 

83 EXPERIMENTS IN NORTHWESTERN 
UNITED STATES AND CANADA 

State College of Washington Project 

During 1943, a series of transmission experiments 
were carried out by a group of workers from the 
State College of Washington under the auspices of 
Division 14, NDRC. 134, 137 ' 164, 228 The first series of 
tests were made in the neighborhood of Spokane over 
14- and 52-mile optical paths and over a 112-mile 
nonoptical path. Later in the same year a transmis¬ 
sion path 20 miles long with receivers both below 
and above the optical horizon was installed on the 
east side of Flathead Lake, Montana. 

Among the tests carried out by this group was an 
experimental telephone communication on 10-cm 
waves which gave excellent results. The earlier 
experiments demonstrated the necessity of having 
detailed data on the refractive index variation in 
low levels and thus led to the development of the 
State College of Washington wired balloon sonde, 
described in the preceding chapter and of basic 
importance for further propagation work. The first 
model of the sonde was used systematically in con¬ 
nection with the Flathead Lake transmission path. 

The location of these experiments has a climate of 
a continental type, there being several mountain 
ranges between these spots and the Pacific coast. 
The air is comparatively dry, and the structure of 
the lowest strata is subject to the large variations 
of temperature and of stability typical of continental 
conditions. 

The general results of these tests are similar in 
many respects to those found at the east coast of 
the United States. The signal types are analogous, 
but the times and frequencies of occurrence are often 
quite different. In the Flathead Lake experiments, 
where strong ducts were often present, signal level 
variations of 50 db were observed for the optical 
path, 55 db for the nonoptical paths. The correlation 
between the observed M curves and the received 
signal strength was extremely close, high signal 
levels being observed when the measured M curves 
showed the presence of a duct; and standard signal 
levels, when the M curve was of the standard type. 
Similar observations were later made many times 
over in other experiments such as those at Massa¬ 
chusetts Bay, already described. 

Figure 10 shows typical signal records in form of 
hourly maxima and minima over a three-day period 
for the 20-mile path on Flathead Lake. Though the 






















66 


TRANSMISSION EXPERIMENTS 



Figure 10. Variation of signal strength over 3 days. Two receivers on S band, Flathead Lake, Montana. 


path itself is entirely over water, the over-water 
trajectory of the air is limited by the dimensions 
of the lake. Both receiving stations are below the 
line of sight, the upper by 91 ft, the lower by 132 ft. 


There is, in this graph, a rather clearcut distinction 
between periods of standard propagation with a 
comparatively limited margin of variability of the 
signal, and periods of superrefraction accompanied 












































































EXPERIMENTS IN NORTHWEST 


67 


by very deep fades. This behavior is found in most 
propagation experiments but is perhaps rarely as 
well marked as in this graph. Another feature of 
interest is the fact that the maximum signal level 
is fairly close to the free space level. This has been 
found to hold approximately in a number of other 
propagation experiments where, in the presence of 
a duct, the maximum received level seems to occur 
not far from the theoretical free space signal level. 
No explanation for this behavior has been given, and 
it may be purely accidental. 

Figure 11 presents, for part of the same period as 


the Canadian Wave Propagation Committee. They 
were started in the last year of the war and are still 
under way at the writing of the present report. 
These tests promise to throw light upon certain 
aspects of the propagation problem that are difficult 
to investigate elsewhere. The equipment is located 
on the prairies of western Canada. The transmission 
path is over terrain that is as near perfectly level 
as can be found. The ground is covered with short 
grass and is without trees or houses. The region forms 
part of a large flat area in which the atmosphere can 
be expected to be much more homogeneous than 



Figure 11 . Values of A; as a measure of M or N gradient for part of period shown in Figure 10. 


shown in Figure 10, the value of Ac as a function of 
time at a point on the transmission path. Here k 
is a measure of the slope of the M curve in the lowest 
strata. Combining equation (17), Chapter 5, and 
equation (4), Chapter 6, we have 1/ka = dM/dh • 
10~ 6 . Thus when k is negative a duct is present. It 
will be seen that the incidence of negative values of k 
correlates well with high signal strength in Figure 10. 

Canadian Experiments 

The Canadian transmission experiments are being 
undertaken by the Tropospheric Subcommittee of 


in more densely populated regions. Extensive meteoro¬ 
logical measurement by means of stationary installa¬ 
tions, captive balloons, and airplanes are being 
carried out simultaneously with the transmission 
experiments. The path is 27 miles long with receivers 
mounted on a tower at several altitudes. The trans¬ 
mitters operate on the S and X bands and are 
pulsed. In addition, radar measurements are being 
undertaken by means of corner reflectors that are 
spaced at regular intervals along a path 45 miles 
long. It may be expected that valuable results will 
soon be received on the completion of these experi¬ 
ments. 










68 


TRANSMISSION EXPERIMENTS 



Figure 12. Signal strength at several elevations as function of distance. (Near San Diego.) 


84 EXPERIMENTS IN 

THE SOUTHWESTERN UNITED STATES 

The Navy Radio and Sound Laboratory at San 
Diego has performed a considerable number of 
propagation experiments which have substantially 
aided our understanding of the phenomena of guided 
propagation. Moreover the meteorological conditions 
found in this part of the United States are rather 
unique; and, while they are not, perhaps, reproduced 
at many other places of the earth, they are so clear- 
cut and regular as to facilitate greatly experimental 
investigations and their interpretations. 

The meteorological conditions at San Diego during 
most of the year are characterized by the presence 
of a high-pressure area and high-level subsidence. 
In more concrete terms, there is a surface stratum 
of comparatively cool and moist air on top of which 
there is a layer of very dry, warm air. The transition 
between the two strata is as sharp as can be found 
anywhere, and the transitional layer is often no more 
than a few hundred feet thick. The height of the 
transition layer above the ground is usually between 
1,000 and 3,000 ft and sometimes as much as 4,000 ft. 


During the winter of 1942 to 1943, a series of 
measurements were made on the intensities of arti¬ 
ficial fixed echoes of a 700-mc radar located near 
San Diego, 125 * 138 and these were compared with 
measured temperature and humidity gradients in 
the lower atmosphere. A pronounced correlation 
between excessive echo ranges and nonstandard 
M gradients at once appeared. The quantitative 
aspects of these correlations will not be discussed 
here since they are very similar to others of this 
type already reported. 

Another set of observations where the receiver 
was located in a plane is shown in Figure 12. 3 The 
receiving antenna was a Yagi, mounted in the nose 
of the plane, records being made when the plane was 
flying over the ocean toward the transmitter which 
was a 500-mc radar. Figure 12 represents the results 
of flights at various altitudes on two different days, 
the maxima of the signal strength curves corres¬ 
ponding to the “lobes” of the transmitter pattern. 
On one of these days a duct was present as shown 
in the inset where Af.is plotted against height. The 
dot-and-dash straight line in this diagram represents 
the condition dh/dM = constant. The most con- 















EXPERIMENTS NEAR SAN DIEGO 


I 


69 


80 MILE LINK SAN PEDRO TO SAN DIEGO 
TRANSMITTER AND RECEIVER AT 100 FT. ALTITUDE 


BASE OF TEMPERATURE INVERSION 

•• °* 


• SAN DIEGO RAYSONDE 
S' e WIRED SONDE 8 AIRPLANE 

* •'<*> 

<f ° 


P V' 



SEPTEM BER OCTOBER 

Figure 13. Signal strength over 80-mile path, San Diego to San Pedro, correlated with height of temperature inversion. 


spicious feature of Figure 12 is the difference between 
the signal distribution in the absence and presence of 
a duct at 500 ft, the lowest level measured, whereas 
the intensities agree fairly well at the higher levels. 
This behavior is in full agreement with the general 
predictions of propagation theory. Nevertheless, the 
detailed interpretation led to a slightly different 


8 

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Figure 14. Computed number of modes trapped versus 
observed field strength, San Diego Bay. 


result from that expected, as was brought out by 
subsequent experimental investigations. 

In 1944 a one-way transmission path was operated 
between San Pedro and San Diego, an over-water 
path 10 * 159 80 miles long with both terminals at an 
elevation of 100 ft, which were thus well below the 
optical horizon. Three fairly low frequencies, 52, 
100, and 547 me, were used. Figure 13 shows a field 
strength diagram of bihourly means for a period of 
about six weeks in the early fall of 1944. At the top 
of these diagrams is shown the height of the base 
of the temperature inversion, which is a quantita¬ 
tive measure of the height of the elevated duct. In 
order to compare these data with the results of duct 
theory, Figure 14 shows the number of lowest modes, 
trapped in the elevated duct, plotted against the 
signal strength. For each point indicated, the number 
of trapped modes is calculated by simple waveguide 
theory from the measured M curves while the field 
strength is that simultaneously measured on the 
transmission path. For the lowest frequency, 52 me, 
the duct is always beyond cutoff and no trapping 
should occur; nevertheless, the field strength record 
shows considerable fluctuation. 

As seen from Figure 14 there is no correlation be- 




























70 


TRANSMISSION EXPERIMENTS 


HEIGHT IN FEET 



50 units through the inversion. 






















































EXPERIMENTS AT ANTIGUA 


71 


tween the field strength and the number of modes 
that, theoretically, are transmitted by the duct. On 
the other hand, there is a very pronounced inverse 
correlation between the height of the inversion layer 
and the strength of the received signal. This is just 
what should be expected on the basis of reflection, as 
distinguished from ray bending, from the elevated 
layer of M inversion. The principle of this reflection 
phenomenon has previously been outlined at the end 
of Chapter 6, Section 6.7. Further study shows that 
the rate of change of the field intensity and its varia¬ 
tion with frequency are just of the magnitude re¬ 
quired by the theory. Figure 15 shows a ray-tracing 
diagram on which the paths of the reflected rays are 
indicated. Summarizing the results of this experi¬ 
ment, it may be said that the phenomenon of reflec¬ 
tion from an elevated layer has been well established 
qualitatively and, in some respects, quantitatively. 
The meteorological conditions at San Diego are rather 
singular, and so far such reflection occurring in a 
systematic fashion has not been described elsewhere 
though indications of similar effects have occasional¬ 
ly been reported. 

Another transmission experiment was made by 
the Navy Radio and Sound Laboratory in the 
Arizona desert in December 1944. 188 The path was 
nonoptical, 47 miles long, and the frequency used 
was 3,200 me. The desert air is extremely dry so that 
the contribution of water vapor to the refractive 
index is small and the change in M owing to changes 
in humidity with height is nearly negligible. During 
the clear nights a pronounced temperature inversion 
develops from radiative cooling of the ground, a 
ground-based duct thus being formed. The received 
field strength varied in close correlation with the 
formation and disappearance of the duct, with a 
pronounced diurnal period. The overall results of 
this experiment are again in excellent qualitative 
agreement with the predictions of the duct theory. 
At the same time the experiment also furnished an 
opportunity for studying the development over land 
of low temperature inversions which are valuable 
for radiometeorological forecasting. 

85 EXPERIMENTS AT ANTIGUA 

Operational experience in the Pacific Ocean led to 
the conclusion that low ducts are very common over 
the ocean surface in subtropical and tropical climates. 
In order to study these ducts, an experiment was un¬ 


dertaken by the Naval Research Laboratory in the 
spring of 1945. 19 ^ The island of Antigua, one of the 
Leeward Islands of the Lesser Antilles in the British 
West Indies, was chosen as the site. The prevailing 
winds there are northeasterly and the air has an over¬ 
water trajectory of several thousand miles before 
arriving at the island and is therefore considered 
characteristic of large portions of the central Atlantic 
and Pacific oceans. There is almost no diurnal and 
only a limited seasonal variation in the air at the 
lowest levels. 

Equipment for the transmission experiments was 
comprised of S-band and X-band sets provided by 
the Radiation Laboratory, MIT. The transmitters 
with parabolic antennas were mounted on a ship at 
heights of 16 and 46 ft. There were two parabolas for 
each height and each frequency, one set pointing to 
the stern and one to the bow, so that measurements 
could be made on both the outward and inward runs 
of the vessel. Receivers were located at heights of 14, 
24, 54, and 94 ft on a tower at the edge of the water. 
Monitoring and automatic recording were similar to 
those used in the transmission experiments pre¬ 
viously described. Records were obtained while the 
ship was traveling away from the receiving station 
and again on its return. Signals could usually be de¬ 
tected up to 190 miles for some combination of 
transmitter and receiver heights. Direction finding 
equipment was used for keeping the ship on its course, 
and fading of the signal caused by the ship’s being 
off course could be readily detected and rectified. 

An extensive program for measuring low-level 
M curves paralleled the transmission measurements. 
Since the weather conditions at Antigua are quite 
steady there is little variation in these curves, as 
shown by two typical ones illustrated in Figure 11 of 
Chapter 7. The low-level duct indicated by these 
graphs has been found present at all times in this 
location. 

Typical field strength records for the S band and 
the X band are shown in Figures 16 and 17, respec¬ 
tively, the most outstanding feature being the varia¬ 
tion of field strength with antenna heights. For the 
S-band transmission, the field strength increases 
slightly with increasing antenna height but not nearly 
so fast as it would under standard conditions. For 
the X band, on the other hand, the field strength, as 
a rule, is increased by lowering the antennas. This 
behavior can be explained on the basis of the mode 
theory of duct propagation as outlined in Chapter 6. 
For the shorter wavelength X band, we have genuine 



72 


TRANSMISSION EXPERIMENTS 


trapping, so that the field strength is greatest when 
the transmitter or receiver or both are in the duct. 
In terms of the height-gain functions of equation 
(27), Chapter 5, it appears that these functions of the 
lowest mode or modes have a pronounced maximum 
in the duct and decrease rapidly above it. For S-band 
transmission there is a transition between the com¬ 
plete cutoff, indicated by a highly simplified wave¬ 
guide theory, and complete trapping. This inter-, 
mediate effect is caused by some leakage of this wave 
train from the duct and the retention by the duct of a 
portion of its wave-guiding properties. The height- 
gain functions, while still much larger in the duct 
than in the case of standard propagation, no longer 
have distinct maxima but show a gradual increase 


with height from the ground. This case is particu¬ 
larly interesting because it clearly exemplifies the 
possible variety of conditions intermediate between 
trapping, as described by the ray tracing of geo¬ 
metrical optics, and the diffraction around the earth’s 
surface characteristic of standard propagation. 

Figure 16 shows two regions with distinctly 
different slopes in the curves of power versus dis¬ 
tance. This probably indicates that two different 
modes predominate in these two regions. The pattern 
shown in Figure 16 can occur if for some distance 
near the ground the height-gain function of the 
second mode is greater than that of the first mode. 
The second mode, however, is attenuated more 
rapidly with distance than the first. At moderate 



Figure 16. Signal strength as function of range. S band, Antigua experiments. 




































































































































ANGLE-OF-ARRIVAL MEASUREMENTS 


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RANGE IN MILES 


















































Figure 17. Signal strength as function of range. X band, Antigua experiments. 


distances from the transmitter the second mode 
prevails, but at greater distances it will become 
smaller than that of the first which decreases less 
rapidly with distance. 

Finally Figure 18 shows a set of curves for attenua¬ 
tion versus distance of the target for an X-band radar 
on Antigua. Again it is evident that, on the whole, 
the lowest elevation of the radar gives the largest 
signal strength. 


86 ANGLE-OF-ARRIYAL MEASUREMENTS 


1 


RADAI 

3 ECHO ^ 

STRENG 
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APRIL IS 

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RANGE 



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4 APR 







RANGE NAUTICAL MILES 


Because the effects of nonstandard propagation 
are most pronounced at great distances from the 


Figure 18. Radar echo strength as function of range. 
X band, Antigua experiments. Target is a PC boat. 
































































































































































74 


TRANSMISSION EXPERIMENTS 


transmitter, they are most important for early warn¬ 
ing radar and communication work. These effects 
were investigated earlier than the question of the 
deviation of the angle of arrival from that prevailing 
in a standard atmosphere. This deviation, though 
small, may nonetheless be significant for fire control 
radars operating in the microwave band. The angle 
of arrival may vary by several minutes of arc because 
of ducts, and this effect was first studied systema¬ 
tically by BTL in 1944. 10,182 

Figure 19 is a schematic view of the receiving 



Figure 19. Sharp-beamed antenna for angle-of-arrival 
measurements. 


antenna used for such measurements. This antenna 
is a section of a parabolic cylinder arranged so that 
its beam, at the center of swing, is directed toward 
the transmitter, this being the angle at which waves 
arrive on a day with standard propagation. The 
antenna measures the vertical angle of arrival, and 
a duplicate antenna rotates about a vertical axis 
and measures the horizontal angle. The antennas 
are periodically swung through an angle which is 



kio SEC^ TIME-► A+B (RECORD 2) 


Figure 20. Typical record of angle-of-arrival measure¬ 
ments. Top, direct ray only. Bottom, direct and ground- 
reflected ray. 

set to include.the largest variations of the angle of 
arrival. Figure 20 shows a typical record of received 
field strength versus time for a periodic swing, the 
upper record representing the presence of a direct 


ray only, and the lower indicating both a direct and 
a ground-reflected ray. 

Observations near New York during the summer 
of 1944 were made on two optical paths 24 and 12.6 
miles long with a common receiving antenna. These 
measurements are estimated to be accurate to 0.04 
degree, and they indicate that the greatest variation 
of the horizontal angle of arrival is 0.10 degree. 
Fluctuations within this magnitude, however, are 
quite common. The maximum in the vertical angle 
for the long path was 0.46 degree above the standard 
for the direct ray and 0.17 degree below the standard 
for the reflected ray. No correlation between depar¬ 
tures from the standard of the direct ray and the 
ground-reflected ray has been observed. When the 
direct ray was 0.46 degree above the standard, it 
was apparently being trapped and no reflected ray 
was observed. The greatest spread observed between 
the direct and reflected rays was 0.75 degree, as 
compared to a standard of 0.35 degree. The variation 
of vertical angle over the short path was less than 
over the long one, the greatest change in angle being 
an increase of 0.28 degree over the standard for the 
direct ray while that of the ground-reflected ray 
was too small to be observed. 

The Evans Signal Laboratory analyzed some 
low-level meteorological records which were made 
simultaneously and in the near vicinity of these 
transmission experiments. The angles of arrival were 
determined by ray-tracing methods and were in 
satisfactory agreement with the observations. The 
difference between angles in standard atmospheres 
of various climates was also analyzed theoretically, 
and the results show that the maximum angular 
deviations are less than the tolerance of present-day 
fire control equipment. 

For early warning radars where the target is 
perhaps 75 to 100 miles away, the difference in 
bending of the rays between standard atmospheres 
of moderate and warm climates becomes appreci¬ 
able. In this case differences in estimated height 
vary by as much as 2,000 ft, if the target height is 
determined by the first signal in the lowest standard 
lobe. 

Measurements of the angle of arrival by BTL 
were continued in 1945, and the results, though not 
yet published, give more details and corroborate the 
previous observations. During the second half of 
1945, the Electrical Engineering Department of the 
University of Texas has embarked on a program 
to study the angle of arrival. 














Chapter 9 

GENERAL METEOROLOGY AND FORECASTING 


91 INTRODUCTION 

I n chapter 5, equation (9) was given for the 
refractive index as 

(n - 1 ) • 10 6 = y ( V - e H -— J . ( 1 ) 

On adding to this the term (h/a) 10 6 the “modified 
refractive index M” of equation (4), Chapter 6 is 
obtained, namely 



When the temperature increases with height, other 
things being constant, n — 1 decreases with height 
and when this decrease is strong enough it will 
outweigh the increase of M caused by the term h/a. 
Similarly, a decrease of moisture with height will 
produce a decrease of n — 1 which, if strong enough, 
will again produce a negative slope of the M curve. 
In Chapter 7 we have dealt with these changes 
purely from the observational viewpoint. Now the 
origin of these variations owing to the physics and 
dynamics of the lower atmosphere will be considered. 
A knowledge of general meteorological conditions 
may enable a trained weather forecaster to predict, 
from weather maps and other pertinent data relat¬ 
ing to the structure of the lower atmosphere, the 
presence of ducts and other meteorological factors 
affecting transmission. 

The first attempts at radio forecasting were made 
as early as 1943 by the British Meteorological Office 
in conjunction with the services operating the radar 
sets along the North Sea and Channel Coast. While 
the correlation between forecasts and observed results 
was imperfect, results were promising enough to 
encourage further studies. Since then, the forecasting 
technique in the British home waters has been 
developed to a considerable degree of effectiveness. 
Studies regarding the relationship between the 
dynamics of the lower atmosphere and radio wave 
propagation have been initiated by the interested 
Services in various parts of the British Empire, 
particularly in Australia where a number of interest¬ 
ing correlations have been discovered. In the United 
States the problem was first systematically attacked 
by the propagation group of the Massachusetts 


Institute of Technology Radiation Laboratory 
[MIT-RL], and at about the same time by the 
Army Air Forces Tactical School in Florida. The 
latter established a training course for radio meteoro¬ 
logical forecasters, a number of whom participated 
in offensive operations in the Pacific at Leyte and 
later. 

In connection with the transmission experiment 
across Massachusetts Bay, which was described in 
Chapter 8, a forecasting unit was established coopera¬ 
tively by MIT-RL, the AAF, and the U. S. Weather 
Bureau at Boston. Regular forecasts were made and 
checked by both meteorological and radio observa¬ 
tions. The pertinent information required for radio 
meteorological forecasting was assembled by a 
number of agencies in England 244 and in this country. 
The most extensive American texts on the subject 
have been issued by Headquarters, Weather Divi¬ 
sion, AAF, 245 and by the Columbia University Wave 
Propagation Group. 157 The latter report, Tropos¬ 
pheric Propagation and Radiometeorology is published 
in Volume 2 of the Summary Technical Report of the 
Committee on Propagation. 

92 ATMOSPHERIC STRATIFICATION 

From the meteorological viewpoint it is convenient 
to distinguish three factors which tend to affect the 
temperature and moisture distribution in the lower 
part of the atmosphere. These factors are known to 
meteorologists as (1) advection, (2) nocturnal cooling 
(over land) and (3) subsidence. 

Advection is a term that designates the horizontal 
displacement of an air mass of specific properties 
over an underlying surface which tends to modify 
the structure of the mass. Thus one speaks of the 
advection of dry polar air over a warm water surface. 
Advection is not the modification of air mass proper¬ 
ties but merely a preliminary to such modification. 

Advection changes the physical characteristics of 
the lower strata of the atmosphere through transfer 
of heat or moisture between the air and the under¬ 
lying ground or sea surface. The operating factor in 
this exchange is turbulence, and a brief review of its 
effects in the atmosphere will be given. 

Nocturnal cooling over land is caused by a loss of 


75 



76 


GENERAL METEOROLOGY AND FORECASTING 


heat from the ground by infrared radiation. The 
cooling thus effected is communicated to the lower 
strata of the atmosphere by means of turbulence. 
Nocturnal cooling occurs to an appreciable degree 
only if the sky is clear. Any layer of clouds will exert 
a “blanketing” effect which reduces the cooling of 
the ground to a small fraction of that for clear nights. 

Subsidence is a meteorological term for the slow 
vertical sinking of air over a very large area. It is 
usually found in regions where barometric highs are 
located. By a dynamic process, too complicated to be 
described here, subsidence often produces a temper¬ 
ature inversion, the air in a subsiding stratum being, 
as a rule, very dry. Subsidence is usually strongest in 
a layer somewhat elevated from the ground, and 
when the dry subsiding mass overlies a moist stratum 
near the ground, a sharp moisture gradient is created 
which is favorable for the formation of the duct. The 
elevated ducts at San Diego are of this type. 

Convection occurs whenever the vertical tempera¬ 
ture gradient exceeds in absolute value the critical 
gradient of about —1C per 100 m. It is usually the 
result of the heating of the ground by the sun’s rays, 
and over land on a hot summer day it may extend to 
great heights in the atmosphere. Since convection 
mixes the air thoroughly,' it establishes small and 
constant moisture gradients throughout the lower 
atmosphere, resulting in a very nearly linear ilfcurve. 
Consequently standard conditions of propagation 
prevail on summer days over land from late morning 
until late afternoon, this being the time when con¬ 
vection is most likely to be present. Often this applies 
also to summer days with a light overcast. 

Frictional turbulence occurs normally in the lowest 
1,000 m of the atmosphere even when convection is 
absent. It is caused by the wind, requires at least 
light winds, and is fully developed with moderate or 
strong winds over land. Since turbulence is caused by 
the roughness of the ground it is less well developed 
over the sea surface. It can safely be assumed that 
over land with moderate or strong winds standard 
propagation conditions prevail because of the reg¬ 
ularizing action of turbulence. 

Temperature inversions occur when the temperature 
of the sea or land surface is appreciably lower than 
that of the air. The temperature transition from the 
ground to the free air takes the form shown in Figure 
1 . The heat and moisture transfer caused by turbu¬ 
lence in a temperature inversion is less simple than 
that in a frictional layer. The turbulent processes in 
inversion regions are highly complex and, as yet, are 



Figure 1. Air temperature versus height for a tempera¬ 
ture inversion. 


not very well explored. It is known, however, that 
the intensity of the vertical transfer of heat and 
moisture is much less than the rate of transfer with 
frictional turbulence and decreases with the vertical 
increase of temperature. In a steep inversion the rate 
of transfer may be many times less than in a fric¬ 
tional layer. This tends to produce a vertical stabiliz¬ 
ation of the air layers in the inversion region. As soon, 
therefore, as a temperature inversion has begun to 
form, the rapid mixing in the lowest layers, usually 
effected by frictional turbulence, stops and is re¬ 
placed by a much more gradual diffusion. 

Assuming that the rate of diffusion has become so 
slow that the transfer of moisture over a height of a 
few hundred feet takes many hours or, perhaps, a 
day or two, when the air in the inversion is dry to 
begin with and flows over the sea or moist land there 
will be established, in such an air mass, a steep mois¬ 
ture lapse, since the water vapor that has been taken 
up by the air near the ground will only gradually 
diffuse into the dry air aloft. Conditions are then 
favorable for the formation of an evaporation duct, 
in addition to whatever tendency toward duct forma¬ 
tion may be caused by the temperature inversion 
itself. 

93 CONDITIONS OVER LAND 

Because of the considerable variation of the ground 
temperature by cooling at night and heating during 
the day, there is to be found over land an alternation 





COASTAL AND MARITIME CONDITIONS 


77 


of convection during the day and conditions of a tem¬ 
perature inversion during the night. There is some 
phase shift in that the atmospheric conditions lag 
about three to four hours behind the sun. The amount 
of nocturnal cooling caused by infrared radiation of 
the ground is very nearly independent of its constitu¬ 
tion. It is, however, strongly reduced by the presence 
of clouds which in turn radiate toward the ground, 
canceling part of the cooling effect. High moisture 
content in the lower atmosphere acts partly in the 
same way and somewhat reduces the heat lost by the 
ground. With a full overcast, nocturnal cooling is 
negligible and normally no temperature inversion 
will be formed. 

In temperate climates temperature inversions alone 
can produce only weak ducts because the effect of 
temperature upon the refractive index is relatively 
small. In the fairly common case, however, where the 
inversion is accompanied by sufficient moisture 
gradient, a strong duct will result. This occurs when 
the air is dry enough to allow evaporation into it 
from the ground. In warmer climates where the transi¬ 
tion between night and day is rapid, evaporation may 
set in early in the morning before the nocturnal in¬ 
version has been completely destroyed by the action 
of the sun. A strong duct will then be formed for a 
short period. 

Fog. Contrary to what might perhaps be expected, 
the formation of fog results generally in a decrease of 
refractive index. For instance, when fog forms by 
nocturnal cooling of the ground, the total amount of 
water in the air remains substantially unchanged, 
although part of the water changes from the gaseous 
to the liquid state. It is found that water suspended 
in the air in the form of drops contributes less to the 
refractive index than the equivalent amount of vapor. 
The formation of fog, therefore, reduces the effective 
contribution of the water vapor to the refractive index. 
If there is a temperature inversion in the fog layer, 
the vapor pressure required for saturation increases 
with height, and a substandard M curve usually 
results. 

With a substandard M curve the electromagnetic 
field near the earth surface is diminished instead of 
increased, a case opposite to that of superrefraction. 
In practice this weakening of the field not uncom¬ 
monly leads to a more or less complete radio blackout. 

Fog, however, does not always produce a sub¬ 
standard M curve although that is usually the case. 
In certain less frequent types of fog, the temperature 
and saturation vapor pressure may be constant or 


increase with height through the fog layer. In this 
event propagation will be standard, or ducts may 
even form occasionally within the fog layer. 

94 COASTAL AND MARITIME CONDITIONS 

Advection is of prime importance near a coast 
where the wind may blow the air from land to sea 
or vice versa. The former case, which is the more 
important in practice, will be considered. A tempera¬ 
ture inversion is formed, if the air from above a 
warmer land surface flows out over a cooler ocean 
surface. Over the land the air will usually have 
attained a state of convective equilibrium with 
correspondingly slow variations of temperature and 
humidity with height. When this air comes in contact 
with the cold water surface a temperature inversion 
is formed which increases gradually as the air 
proceeds over the water. Thus the inversion is the 
more pronounced, the greater the distance from the 
shore. Eventually, however, at very large distances, 
equilibrium between the air and the water surface 
will again be reached. 

The temperature inversion formed during this 
process would in itself give rise to only a compara¬ 
tively weak duct. When, however, the air is dry, 
evaporation from the sea surface takes place simul¬ 
taneously with heat transfer, and a fairly strong 
negative humidity gradient is established in the 
lowest layers. This combination of temperature inver¬ 
sion and moisture gradient is very favorable for the 
formation of a pronounced duct off shore. 


T 0 « 32 C E 0 * 12.3 MILLIBAR 
T w * 22 C E w * 26.5 MILLIBAR 



Figure 2. Successive M curves resulting from modifica¬ 
tion of warm dry air over cool moist surface. Zero time 
corresponds to the coastline; 1/4 hr, 1/2 hr, etc. refer to 
the time the air has been over water. 

The progressive formation of an advection duct, 
created by the mechanism just outlined, is shown 























78 


GENERAL METEOROLOGY AND FORECASTING 


schematically in Figure 2. The successive M curves 
correspond to a series of time intervals measured 
from the passage of the air over the shore line. The 
increase of the duct toward the maximum and the 
subsequent flattening of the M curve as the air 
approaches a new state of equilibrium is clearly seen 
from the figure. 

Duct formation in such a case depends on two 
quantities: (1) the excess of the unmodified air 
temperature above the water temperature, and (2) 
the humidity deficit, that is, the difference between 
the saturation vapor pressure corresponding to the 
water temperature and the actual water vapor pres¬ 
sure in the unmodified air. The problem can be 
treated by means of the mathematical theory of 
diffusion in a turbulent medium, and a considerable 
amount of effort has been spent in investigating this 
type of advective duct. Extensive mathematical 
work has been carried out in England 200 based 
primarily on the large body of data on atmospheric 
diffusion gathered in connection with chemical 
warfare problems. 197 In the United States such 
ducts have been studied very extensively in con¬ 
nection with the propagation experiments in Massa¬ 
chusetts Bay where conditions are favorable for 
their formation. 201,204 

Another phenomenon often responsible for ducts 
in coastal regions is the land and sea breeze. This 
type of wind is of thermal origin and is produced 
by temperature differences between land and sea. 
During the day, when the land gets warmer than 
the sea, the air over the land rises and that over the 
sea descends, thus causing a circulation in which 
the air in the lowest layers flows from sea to land. 
This is the sea breeze. Vice versa, during the night 
the land becomes colder than the sea, and circulation 
is in the reverse direction, creating the land breeze. 
As a rule this type of phenomenon is extremely 
shallow, and the winds do not extend above a few 
hundred feet at the most. A sea breeze modifies the 
advective conditions described above in various 
ways, and extremely strong ducts have occasionally 
been observed under sea breeze conditions. The land 
and sea breezes are of a strictly local nature and in 
some cases will extend only a few miles to land or 
sea from the shore. Nevertheless this region may be 
an important part of the radiation trajectory of 
coastal radars. These breezes develop only under 
fairly calm conditions; they are wiped out by a 
moderate or strong wind. 

The advective ducts of the types described here 


are by their very nature of only limited horizontal 
extent. The horizontal variation of refractive index 
presents a problem that till now has not been sys¬ 
tematically studied from either the experimental or 
the theoretical angle. 

A particular type of duct has been discovered in 
purely maritime air, that is, air which has had an 
extremely long sea trajectory and thus should have 
reached an approximately steady state of diffusion 
relative to the underlying sea surface. The Antigua 
experiments described in the preceding chapter reveal 
the existence of a type of low duct which seems to be 
characteristic of maritime air. It appears probable 
that similar ducts are permanent in the oceanic 
regions of many parts of the earth. The relative 
humidity of the air at Antigua was found to be 60 
to 80 per cent, indicating that a continuous upward 
diffusion of moisture must take place, since the air 
immediately adjacent to the water surface is always 
practically saturated. On the other hand, there is 
little difference between the air and sea tempera¬ 
tures in this case, the ocean being about 25 C while 
the air temperature varies between 23 and 26 C. 
The ducts are therefore caused solely by the varia¬ 
tion of water vapor in the lowest layers and are 
much lower than the advective ducts described 
before, their height rarely exceeding 40 ft. Typical 
M curves have been shown in Chapter 7, and, for 
the particular effects caused by the low height of 
these ducts, we refer to the discussion of the experi¬ 
mental results. 

The diurnal change of ocean temperature is 
insignificant, except in extremely shallow water, and 
therefore, at some distance from the coast, propaga¬ 
tion conditions do not show any appreciable diurnal 
variation. 

95 DYNAMIC EFFECTS 

The physical processes in the lower strata of the 
atmosphere which determine the formation of ducts 
are to a considerable extent controlled by the large- 
scale dynamics of the atmosphere. It is therefore 
often possible to make at least a qualitative forecast 
of propagation conditions on the basis of a knowledge 
of the synoptic weather situation. An example in 
point is the diurnal variation over land in clear 
weather from standard conditions during the day 
to duct conditions in the latter part of the night 
and the early morning hours. 

Conditions in a barometric low pressure area 



WORLD SURVEY 


79 


generally favor standard propagation. Winds are 
usually strong or at least moderate resulting in a 
well-mixed layer of frictional turbulence. Local 
thermal stratifications are destroyed, and abnormal 
moisture gradients will not develop because of the 
intense turbulent mixing. The sky is frequently 
overcast in the low pressure area and nocturnal 
cooling therefore is often negligible. 

On the other hand, meteorological conditions in 
a high pressure area are frequently favorable for 
the formation of ducts. The sky is commonly clear, 
thus giving rise to pronounced nocturnal cooling of 
the ground and to the attendant formation of a 
temperature inversion in the lowest layers. This, 
again, often gives rise, by evaporation, to steep 
moisture gradients within the inversion layer result¬ 
ing in the formation of ducts in the manner already 
described. Winds in high pressure areas are often 
slight, or a calm prevails, resulting in a formation 
of local thermal stratifications and of land and sea 
breezes. 

One of the prime phenomena conducive to non¬ 
standard propagation conditions in a barometric 
high is subsidence, already described. Subsidence is 
closely connected to high pressure areas on the 
weather map and is always found in such areas, but 
it is not always intense enough to produce an 
inversion. The typical pattern of air flow in a baro- 


ILLUSTRATING SUBSIDENCE (SINKING) iN HIGH PRESSURE AREA 


AS IT APPEARS 
ON THE WEATH- 



I \ 


INVERSION REGION 


VERTICAL 

CROSS 

SECTION 




UNAFFECTED AIR 


Figure 3. Schematic diagram illustrating subsidence in 
a region of high barometric pressure. 

metric high is shown in Figure 3 in both horizontal 
projection and vertical cross section. 

The air in the lower parts of a region of subsidence 
is very dry because it has descended from a high 
level in the atmosphere where the temperature is low 
and hence the saturation vapor pressure is small. 


If such air is located over a surface capable of evap¬ 
oration such as the ocean, a steep moisture gradient 
may be established at some level above the ground. 
This is the most common mechanism for the forma¬ 
tion of elevated ducts. Quite often subsidence com¬ 
bines with some or the other effects mentioned 
earlier enhancing their tendency toward the forma¬ 
tion of the duct. The elevated ducts found in the San 
Diego region are perhaps the most outstanding exam¬ 
ple of this type of dynamically induced stratification. 

The effect of fronts in the atmosphere upon propa¬ 
gation does not seem to be very pronounced. This is 
probably due to the fact that in a front the transition 
between warm and cold air is comparatively gradual 
extending over a height of perhaps 1 km. In the Eng¬ 
lish propagation experiments some effects of fronts 
have indicated slightly substandard conditions with 
warm fronts and slightly superstandard conditions 
with cold fronts. Often, however, the effect of fronts 
upon radio propagation is negligible. This, of course, 
refers only to the frontal region itself and not to the 
change in air mass and attendant propagation con¬ 
ditions connected with the passage of a front. 


96 WORLD SURVEY 

It clearly appears from the preceding sections 
that climate has a fundamental influence on the 
nature of propagation conditions. A systematic 
attack on the problem of the occurrence of ducts over 
the ocean has been made in England on a world-wide 
scale. 250 Monthly maps based on estimates drawn 
from general low-level weather data, giving regions 
of the most frequent occurrence of superrefraction 
and substandard refraction, were issued. However, 
these need much further checking by actual observa¬ 
tions. The propagation features of some important 
parts of the world where some knowledge has been 
accumulated is outlined briefly below. 

Atlantic Coast of the United States. Along the north¬ 
ern part of this coast superrefraction is common in 
summer, while in the Florida region the seasonal 
trend is reversed, a maximum occurring in the winter 
season. 

Western Europe. On the eastern side of the Atlantic, 
around the British Isles and in the North Sea, there 
is a pronounced maximum in the summer months. 
Conditions in the Irish Sea, the Channel, and East 
Anglia have been studied by observing the appear¬ 
ance or nonappearance of fixed echoes. Additional 








80 


GENERAL METEOROLOGY AND FORECASTING 


data based on one-way communication confirmed the 
radar investigations. 

Mediterranean Region. The campaign in this region 
provided good opportunities for the study of local 
propagation conditions. The seasonal variation is 
very marked, with superrefraction more or less the 
rule in summer, while conditions are approximately 
standard in the winter. An illuminating example is 
provided by observations from Malta, where the 
island of Pantelleria was visible 90 per cent of the 
time during the summer months, although it lies be¬ 
yond the normal radar range. 

Superrefraction in the Central Mediterranean area 
is caused by the flow of warm, dry air from the south 
(sirocco) which moves across the ocean, thus pro¬ 
viding an excellent opportunity for the formation of 
ducts. In the winter, however, the climate in the 
Central Mediterranean is more or less a reflection of 
Atlantic conditions and hence is not favorable for 
duct formation. 

The Arabian Sea. Observations covering a con¬ 
siderable period are available from stations in India, 
the inlet to the Persian Gulf, and the Gulf of Aden. 
The dominating meteorological factor in this region 
is the southwest monsoon which blows from early 
June to mid-September and covers the whole Arabian 
Sea with moist equatorial air up to considerable 
heights. Where this meteorological situation is fully 
developed, no occurrence of superrefraction is to be 
expected. In accordance with this expectation, all the 
stations along the west side of the Deccan report 
normal conditions during the southwest monsoon 
season. During the dry season, on the other hand, 
conditions are very different. Superrefraction then is 
the rule rather than the exception, and on some oc¬ 
casions very long ranges, up to 1,500 miles (Oman, 
Somaliland), have been observed with fixed echoes 
on 200-mc radar, based near Bombay. 

When the southwest monsoon sets in early in 
June, superrefraction disappears on the Indian side 
of the Arabian Sea. However, along the western 
coasts conditions favoring superrefraction may still 
linger. This has been reported from the Gulf of 
Aden and the Strait of Hormuz, both of which lie 
on the outskirts of the main region dominated by 
the monsoon. The Strait of Hormuz is particularly 
interesting as the monsoon there has to contest 
against the “shanm!” from the north. The Strait 
itself falls at the boundary between the two wind 
systems, forming a front, with the dry and warm 
shamal on top, and the colder, humid monsoon 


underneath. As a consequence, conditions are favor¬ 
able for the formation of an extensive radio duct, 
which is of great importance for radar operation in 
the Strait. 

The Bay of Bengal. Such reports as are available 
from this region indicate that the seasonal trend is 
the same as in the Arabian Sea, with normal condi¬ 
tions occurring during the season of the southwest 
monsoon, while superrefraction is found during the 
dry season. It appears, however, that superrefraction 
is much less pronounced than on the northwest side 
of the peninsula. 

The Pacific Ocean. This region appears to be the 
one where, up to the present, least precise knowledge 
is available. There seems, however, to be definite 
evidence for the frequent occurrence of superrefrac¬ 
tion at some locations, e.g., Guadalcanal, the east 
coast of Australia, around New Guinea, and on 
Saipan. Along the Pacific coast of the United States, 
observations indicate frequent occurrence of super¬ 
refraction, but no statement as to its seasonal trend 
seems to be available. The same holds good for the 
region near Australia. 

In the tropics there is a very strong and persistent 
seasonal temperature inversion, the so-called trade 
wind inversion. It has no doubt a very profound 
influence on the operation of radar and short wave 
communication equipment in the Pacific theater. 

97 RADAR FORECASTING 

The forecasting of propagation conditions for early 
warning radars is of great operational significance be¬ 
cause ranges for airplane as well as ship targets often 
vary by as much as a factor of 2 or more depending 
on the weather conditions. Forecasting is based on 
the general meteorological principles presented above 
which can be organized into a system of standard 
procedures for the prediction of propagation in a 
given area. 244,253,255 It is usually quite difficult to 
make a quantitative forecast of such parameters as 
duct height, but this has been tried with a fair 
degree of success. 

A radio forecast is made by first taking the general 
synoptic weather situation as presented on a weather 
map and including such upper air data as may be 
available. Usually one forecast cannot be applied to 
more than a limited area of specific local conditions; 
fortunately such a forecast is in general adequate for 
the area covered by one or a few radar sets. The 



RADAR FORECASTING 


81 


formation of ducts depends principally on the tem¬ 
perature difference between the air and the ground 
or sea surface and on the humidity of the air. Data 
on sea temperature, which is usually fairly constant, 
are collected while over land it is necessary to obtain 
data on the diurnal variation of the soil temperature. 
Wind velocities may be gathered from the weather 
map, and the trajectory of the air previous to and 
during the forecast period can then be determined. 
If the relative humidity of the air is known, it is 
possible from the theories at hand to draw estimated 
curves of the temperature and moisture variation 
in the lowest layers. From these an estimated M 
curve is obtained. The success of this method depends 
to a large degree upon the familiarity of the forecaster 
with local conditions. 

The forecasting of advective ducts over the ocean 


is the main problem in which radio forecasting 
requires other tools than those used for ordinary 
weather forecasting; but most other problems are 
closely similar to those presented by conventional 
practice, among which are the forecasting of subsi¬ 
dence from upper air meteorological data, the 
forecasting of nocturnal temperature inversions in 
dry climates, and the forecasting of standard 
propagation conditions. 

In order to facilitate weather forecasting in the 
Pacific, where data have been very scanty during 
the war, a system has been worked out whereby 
localities in the Pacific area are compared to those 
of closely similar climatic and meteorological charac¬ 
ter in the Atlantic. A rough estimate of propagation 
conditions to be expected may be derived there¬ 
from. 25 ' 215 



Chapter 10 

SCATTERING AND ABSORPTION OF MICROWAVES 


T he object of the present chapter is to summarize 
the status of absorption and scattering of micro- 
waves by different solid obstacles, by liquid water 
or ice particles floating or falling in the atmosphere 
like those present in clouds, fog, rain, hail, and snow. 
The absorption of microwaves by the atmospheric 
gases as well as the aforementioned meteorological 
elements will also be summarized here. 

The following grouping of the material included 
suggests itself naturally: absorption and radar cross 
section; targets (planes, ships); absorption and scat¬ 
tering by rain, hail, snow, clouds, and fog; and 
absorption by the atmospheric gases, oxygen, and 
water vapor. 


101 ABSORPTION AND RADAR 
CROSS SECTION 

Any object irradiated by electromagnetic waves 
will in general remove energy from the incident 
beam both by absorption and by scattering. The 
absorbed energy is transformed into heat in the 
body, while the scattered energy appears in the form 
of radiation propagated generally in every direction 
around the scatterer as the source. 

Let us call P a the power removed from the beam 
through the internal absorption of the object. Its 
absorption cross section is defined by 



where W t is the power density in the incident beam, 
that is, the power passing a unit cross-sectional area. 

Similarly, if P s is the total power removed from 
the beam through scattering in every direction, then 
the scattering cross section associated with this 
object is 



The value of S gives information about the total 
scattered energy, but this is not directly useful in 
radar work because one is interested only in that 
fraction of the total scattered power which travels 
in the direction of the receiver. One wants then a 


parameter involving the scattered power per unit 
area W r at the radar receiver instead of the total. 
If the target is an isotropic scatterer, 


d being the distance from the target to the receiver. 
The scattering cross section can thus be written as 

W 

S = 4tt d 2 ^ . (4) 

Wi 

For targets other than isotropic scatterers, however, 
this procedure fails since one cannot say that the 
power per unit area at the radar is P s /4ird 2 . Never¬ 
theless, it is useful to define a parameter, 

W 

= (5) 

which is called the radar cross section in analogy 
with the scattering cross section S of an isotropic 
scatterer. This cross section a may be thought of 
as the scattering cross section which the target in 
question would have if it scattered as much energy 
in all directions as it actually does scatter in the 
direction of the radar receiver. For an isotropic 
scatterer a = S, but in general it does not. 

It can be shown a that the ratio of the received 
power P 2 to the output power Pi is given by 



The gains Gi, G 2 and path factor A v are defined in 
Volume 3, Chapter 2, and X is the wavelength of the 
radiation used. (See also Volume 3, Chapter 9.) This 
formula can be used for the determination of a. Or 
if a is known, it may serve to calculate the possible 
range. (It may be noted here that sometimes aA* 
is called radar cross section.) Also, a characteristic 
length L, sometimes called the scattering coefficient, 
is occasionally defined in relation to <r by 

(7 = 4 ttL 2 . (7) 

For simple targets a may be calculated. Table 1 
contains a few calculated radar cross sections. 


a See Volume 3 of the Summary Technical Report of the 
Committee on Propagation. 


82 



AIRCRAFT TARGETS 


83 


Table 1. Radar cross sections. 


Targets 

Condition 

Radar 

cross section 

Conducting 

sphere, 

X < < a 

7r a 2 

radius a 

X > > a 

1447r 5 a 6 

X 4 

0 

Metallic plate, 

All dimen¬ 

4tdS 2 

area S 

sions > > X 

X 2 

Cylinder, 

Axis of cylinder 

irdl 2 

diameter = d 

parallel to 


length = l 

electric field, X 
<<d, \ << l 


Matched load 

Oriented parallel 

9X 2 

dipole 

to the incident 
electric field 

16tt 

Shorted dipole 

Oriented parallel 

9X 2 


to the incident 
electric field 

4t r 


Corner reflector 47 taS 2 

X 2 

S = cross section 
of triply 
reflected beam 


Triangular 

corner 

reflector 


L = length of 
reflector’s edge. 

0 = angle between 
direction of incidence 
and axis of symmetry 
of reflector 


4t rL 4 
3\ 2 


(1 -0.0076 0 2 ) 


Square corner 
reflector 


^^( 1 - 0.0274 ») 


102 AIRCRAFT TARGETS 

Diagrams showing the dependence of a on the 
orientation of the aircraft indicate very large and 
irregular fluctuations. The radar cross section can 
change by 100 to 1 with a change of aspect of only 
a few degrees. These varying values of the radar 
cross section are dependent on wavelength, polari¬ 
zation, details of plane design, etc. Reflection pat¬ 
terns such as shown in Figure 1 have been measured 
in the laboratory for a few simplified models. Actually 
an observer would see only the time average of the 
radar cross section of a plane, and it is only this 
average value which is of operational importance. 

Table 2 gives measured values of <j for various 
aircraft. These are the values to be used in equation 
(6). As far as is known, these empirical cross sections 


210 


200 



Figure 1 . Aspect diagram of a B-17E at 5 degrees 
above horizon. 


are independent of wavelength. This result may be 
interpreted to mean that a plane in motion behaves 
more or less like a collection of good reflecting 
surfaces oriented at random. It is worth noting in 
this connection that the radar cross section of a 
circular plate of radius a, whose normal is at an 
angle 0 with the direction of incidence, is 


a = 7r a 2 


[cot 6 X Ji sin 0^ 


( 8 ) 


Table 2. Airplane radar cross sections. 


Airplane 

<r, sq m 

<r, sq ft 

SNC 

3.9 

42 

SNJ 

5.0 

54 

OS-2U 

9.5 

100 

Taylor craft 

9.5 

100 

CESSNA 

9.5 

100 

0-47 

10 

110 

AT-11 

11 

120 

SWB 

13 

140 

15-D (Curtiss Wright) 

23 

250 

J2F 

25 

260 

JRF 

30 

320 

PBY 

31 

340 

B-18 

36 

380 

B-17 

45 

480 

B-29 

67 

710 








































84 


SCATTERING AND ABSORPTION OF MICROWAVES 


where J\ is the first order Bessel function of the first 
kind. The maximum of <7 occurs for 0 = 0, when 
equation (8) reduces to 


<7 


4t r 3 a 4 
X 2 


( 9 ) 


This sharp maximum of a at 9 = 0 is the phenom¬ 
enon of specular reflection. The average value of 
<7 over all values of 6 turns out to be 

0”avg — " (19) 


This result is independent of wavelength and suggests 
that a large number of specularly reflecting surfaces 
oriented at random will have a cross section inde¬ 
pendent of X, or that a few surfaces of rapidly chang¬ 
ing orientation may have this property. The lack 
of dependence of wavelength of aircraft radar cross 
sections might be understood on the basis of these 
results. 


103 SHIP TARGETS 

A ship being a collection of both complicated and 
flat surfaces, a rigorous computation of the radar 
cross section of any given ship of known design is 
not feasible. Nevertheless, the Naval Research 
Laboratory workers have been able to give a good 
account of these problems. 374,376,388,392,417,421 

The path factor in the formula (6) raised to the 
fourth power is 

a % = - ^- 0(4 - c ° s « o) J, (11) 

whcre . M,JI 
= ~U~ ’ 

hi = antenna height, 

11 = height of ship above water 
including superstructure. 

The above result follows by integrating the received 
power over the height H, assuming perfect reflection 
from sea. 

It is seen in equation (11) that whether 8 0 < it, 
the region called the “far zone,” or 8 0 > tt, the “near # 
zone” (short ranges), materially affects the qualita¬ 
tive behavior of the factor A\. In the latter region 
A* ^ 6 . 

The radar cross section of a ship which does not 
exhibit marked specular reflection is given roughly by 


<7 


B 2 H 


( 12 ) 


where a = dimensionless constant dependent 
on ship design, 

B = the breadth of the aspect under 
observation, 

H = height of ship above water including 
superstructure. 


The approximate values of a to be used are indicated 
in Table 3. 


Table 3. Ship targets. 


Type of ship 

a 

Remarks 

Battleship 

0.1 


Cruiser 

0.1 


Aircraft carrier 

0.05 

Except at direct 
broadside aspect 

Submarine 

0.01 



In Tables 4 to 7, values of a computed from 
equation (12) are called theoretical values. Experi¬ 
mental values are computed from observations made 
by the Naval Research Laboratory workers with 
each quantity the mean of several observations. The 
200-mc experimental result is unexpectedly low while 
the values at the higher frequencies are a little 
higher than would be anticipated. This points to the 
existence of some specular reflection for this ship, 
which would not be surprising in view of its great 
size. Considering the uncertainty in the experimental 
values, the agreement with the theoretical results is 
not unsatisfactory and bears out the assumed 
dependence on wavelength. 

The aircraft carrier shows pronounced specular 
reflection at the direct broadside aspect, particularly 
at the higher frequencies. These values of a are 


Table 4. Radar cross section of a battleship (BB-63), 
broadside aspect, a = 0.1, B = 270 m, H — 24 m. 


/(me) 

a (exp), sq m 

a (theory), sq m 

200 

0.12 X 10 5 

1.9 X 10 5 

700 

10.2 X 10 5 

6.8 X 10 5 

970 

15. X 10 5 

9.4 X 10 s 

3,060 

110. X 10 5 

30. X 10 5 

Table 5. Radar 

cross section of a 

cruiser (CL-87), 

broadside aspect, a 

= 0.1, B = 180 m 

, H = 24 m. 

/(me) 

<r (exp), sq m 

a (theory), sq m 

100 

2.45 X 10 4 

2.6 X 10 4 

200 

5.06 X 10 4 

5.2 X 10 4 

700 

7.79 X 10 4 

18.1 X 10 4 

970 

28.4 X 10 4 

25.1 X 10 4 

3,060 

102.2 X 10 4 

79.3 X 10 4 


















ABSORPTION AND SCATTERING BY CLOUDS, FOG, RAIN, HAIL, AND SNOW 


85 


Table 6. Radar cross section of submarine (SS-171), 
broadside aspect, a = 0.01, B = 83 m, H = 7.6 m. 


/(me) 

<r(exp), sq m 

a (theory), sq m 

200 

700 

3,060 

3.0 X 10 2 
18.7 X 10 2 
71.4 X 10 2 

3.5 X 10 2 

12.2 X 10 2 

53.4 X 10 2 

Table 7. Radar cross section of aircraft carrier (CV-36), 
near broadside aspect, a. = 0.05, B = 250 m, H = 46 m. 

/(me) 

tr(exp), sq m 

a (theory), sq m 

200 

700 

970 

3,060 

0.22 X 10 5 
2.6 X 10 5 
6.3 X 10 5 
11.3 X 10 5 

0.96 X 10 5 

3.4 X 10 5 

4.6 X 10 5 

14.4 X 10 5 


typical of the ship for aspects other than direct 
broadside. 

In Table 8, the same ship is analyzed at direct 
broadside. No theoretical calculation of cr has been 
attempted because of a lack of sufficient data from 
other ships of this type. The column XV is near 


Table 8. Radar cross section of aircraft carrier (CV-36), 
direct broadside aspect. 


/(me) 

<r(exp), sq m 

X 2 <t (exp) 

200 

0.055 X 10 7 

1.2 X 10 6 

700 

1.0 X 10 7 

1.8 X 10 6 

970 

5.0 X 10 7 

4.8 X 10 6 

3,060 

7.1 X 10 7 

7.1 X 10 6 


enough to a constant to indicate the existence of 
specular reflection. Since the hull at broadside can 
be considered as a flat surface, specular reflection is 
to be expected under normal incidence with a radar 
cross section proportional to 1/X 2 as indicated by 
equation (9). 

In view of the complicated reflecting properties of 
targets of operational interest, it may be said that 
the experimental results can be considered as being 
in fair agreement with theoretical predictions. 

104 ABSORPTION AND SCATTERING 
BY CLOUDS, FOG, RAIN, HAIL, AND SNOW 

The theory of the scattering and absorption of 
microwaves by a collection of spherical particles of 
known concentration, size, distribution, and given 
dielectric properties was completely worked out 
before systematic experimental work was done on 
these phenomena. 258,277,279 The electromagnetic 
theory predicts that the total scattering cross section 
of a sphere of given electrical properties is 


& — 2tt E ^ n 1) 0 a » I 2 + l&» ! 2 ) cm2 > (13) 

71= 1 

where X is the wavelength in centimeters of the 
incident radiation in air and a n and b n are the so- 
called scattering amplitudes associated with the 
magnetic and electric 2n-poles induced in the sphere 
by the incident electromagnetic field. Similarly the 
absorption cross section of a sphere defined as the 
ratio of the total power removed from the incident 
beam both by “internal absorption” (heating) and 
by scattering is 

X 2 

A = ^ (“Re) 2j ( 2re + !) (“» + b n ) • (14) 

n = l 

Here Re means “Real part of . . . .” The complex 
scattering amplitudes depend on the dielectric con¬ 
stants of the sphere, its diameter, and the wavelength 
of the incident radiation. The observations which 
are available seem to indicate that a collection of 
spherical particles with random distribution scatter 
microwaves incoherently, although under certain 
circumstances, existing for very short time intervals, 
they may scatter coherently. 419 On the assumption 
of incoherent scattering, given a collection of 
spherical particles of diameters D h D 2 , 

D n , whose number per unit volume or cc is n h n 2 , • • •, 
%,*•*, n HJ the scattering cross section of such a 
collection per unit volume or the absorption coeffi¬ 
cient due to scattering is 

n 

a s = 4.343 X 10 5 tii Si db/km , (15) 

i =1 

where S t is the scattering cross section of one drop 
of diameter D t centimeters, and the summation 
extends over all possible drops present in the col¬ 
lection. Similarly, the “absorption coefficient” or 
“attenuation” associated with the absorption cross 
section A t (sphere of diameter D t ) defined by 
equation (14) is 

n 

a a = 4.343 X 10 s ^ n, A, db/km . (16) 

1=1 

Rain and Hail Absorption 

In order to compute the theoretical absorption 
coefficient of a rain or thunderhead (heavy storm 
cloud) one has to know the raindrop size distribution, 
since the computation of the cross sections for one 
spherical drop is straightforward provided its dielec¬ 
tric properties are known. The greatest uncertainties 















86 


SCATTERING AND ABSORPTION OF MICROWAVES 


in the theoretical predictions of scattering or absorp¬ 
tion by rain are due to the relatively limited knowl¬ 
edge of drop size distributions in rains of different 
rates of fall. There is no evidence that a rain with a 
known rate of fall has a unique drop size distribution 
though the latest studies on this problem seem to 
indicate that a certain most probable drop size 
distribution can be attached to a rain of given rate 
of fall. 446 Results of this study are included in Table 
9. On the basis of these results the absorption cross 

Table 9. Drop size distribution. 


Percentage of total volume 


mm/hr 


D, cm 

0.25 

1.25 

2.5 

12.5 

25 

50 

100 

150 

0.05 

28.0 

10.9 

7.3 

2.6 

1.7 

1.2 

1.0 

1.0 

0.10 

50.1 

37.1 

27.8 

11.5 

7.6 

5.4 

4.6 

4.1 

0.15 

18.2 

31.3 

32.8 

24.5 

18.4 

12.5 

8.8 

7.6 

0.20 

3.0 

13.5 

19.0 

25.4 

23.9 

19.9 

13.9 

11.7 

0.25 

0.7 

4.9 

7.9 

17.3 

19.9 

20.9 

17.1 

13.9 

0.30 


1.5 

3.3 

10.1 

12.8 

15.6 

18.4 

17.7 

0.35 


0.6 

1.1 

4.3 

8.2 

10.9 

15.0 

16.1 

0.40 


0.2 

0.6 

2.3 

3.5 

6.7 

9.0 

11.9 

0.45 



0.2 

1.2 

2.1 

3.3 

5.8 

7.7 

0.50 




0.6 

1.1 

1.8 

3.0 

3.6 

0.55 




0.2 

0.5 

1.1 

1.7 

2.2 

0.60 





0.3 

0.5 

1.0 

1.2 

0.65 






0.2 

0.7 

1.0 

0.70 








0.3 


section of raindrops of different size has been com¬ 
puted for use in Table 10. This table gives the decibel 
attenuation per kilometer in rains of different rates 
of fall and for radiation of wavelengths between 
0.3 and 10 cm. In Table 11, similar to Table 10, 
another set of results is contained for rains of 
measured drop size distributions. This table is 
extended to include radiations of wavelengths up to 
100 cm. It seems equally interesting to give a graphi¬ 
cal representation of those results. Figure 2 corres¬ 
ponds to Table 10 and Figure 3 to Table 11. All 
these data refer to raindrops at 18 C. 



MN CM 


Figure 2. Graphical presentation of data given in Table 

10 . 

Since the scattering coefficients a n and b n depend 
on the temperature, because of its effect on the 
dielectric properties of water, it seems important to 
evaluate the attenuation of rains whose drops are 
at temperatures different from those included in the 
preceding tables. Table 12 contains the necessary 
data relative to the changes of attenuation with 
temperature and is to be used primarily in connec¬ 
tion with Table 10. 

It will suffice to mention here that, for waves 
larger than about 3 cm, the attenuation produced 
by hail of the same water precipitation rate as a rain 
will be but a few per cent of the rain attenuation. 
At shorter waves, in the millimeter region, hail 
attenuation may become larger than that of rain. 
Similarly the attenuation of snow should be con¬ 
siderably less than rain; however, Canadian reports 
indicate approximately the same value for the same 
water content. 

As mentioned above, the whole theory of attenua¬ 
tion is based on equation (14). The formulas giving 


Table 10. Attenuation in decibels per kilometer for different rates of precipitation of rain. Temperature 18 C, X in cm. 277 


Attenuation, db/km. 


P, 


mm/hr 

X = 0.3 

X = 0.4 

X = 0.5 

X = 0.6 

0.25 

0.305 

0.230 

0.160 

0.106 

1.25 

1.15 

0.929 

0.720 

0.549 

2.5 

1.98 

1.66 

1.34 

1.08 

12.5 

6.72 

6.04 

5.36 

4.72 

25 

11.3 

10.4 

9.49 

8.59 

50 

19.2 

17.9 

16.6 

15.3 

100 

33.3 

31.1 

29.0 

27.0 

150 

46.0 

43.7 

40.5 

37.9 


X = 1.0 

X = 1.25 

X = 3.0 

X = 3.2 

X = 10 

0.037 

0.0215 

0.00224 

0.0019 

0.0000997 

0.228 

0.136 

0.0161 

0.0117 

0.000416 

0.492 

0.298 

0.0388 

0.0317 

0.000785 

2.73 

1.77 

0.285 

0.238 

0.00364 

5.47 

3.72 

0.656 

0.555 

0.00728 

10.7 

7.67 

1.46 

1.26 

0.0149 

20.0 

15.3 

3.24 

2.80 

0.0311 

28.8 

22.8 

4.97 

4.39 

0.0481 









































ABSORPTION AND SCATTERING BY CLOUDS, FOG, RAIN, HAIL, AND SNOW 


87 


Table 11. Attenuation in rains of known drop size distribution and rate of fall (decibels per kilometer). 

— ■ ■ - . ' ■ ' - — - ■ / ■ _ _ 

Wavelength X, cm 

mm/hr 1.25 3 5 8 10 15 Distribution 


2.46 

1.93 

10" 1 

4.92 

10~ 2 

4.24 

10 -3 

4.0 

3.18 

10- 1 

8.63 

lO- 2 

7.11 

IO -3 

6.0 

6.15 

10- 1 

1.92 

10" 1 

1.25 

10-2 

15.2 

2.12 


6.13 

10" 1 

5.91 

10-2 

18.7 

2.37 


8.01 

10" 1 

5.13 

10-2 

22.6 

2.40 


7.28 

10" 1 

5.29 

lO" 2 

34.3 

4.51 


1.28 


1.12 

10- 1 

43.1 

6.17 


1.64 


1.65 

10- 1 


1.23 

10~ 3 

7.34 

10- 4 

2.80 

10" 4 

A 

2.04 

lO" 3 

1.19 

lO" 3 

4.69 

10 -4 

C 

3.02 

lO” 3 

1.67 

lO -3 

5.84 

io - 4 

D 

1.17 

lO” 2 

5.68 

lO" 3 

1.69 

10-3 

E 

1.10 

10-2 

6.46 

lO" 3 

1.85 

10-3 

F 

1.21 

10-2 

6.96 

lO" 3 

2.27 

10-3 

G 

2.32 

10-2 

1.17 

lO" 2 

3.64 

IO” 3 

H 

3.33 

10-2 

1.62 

10-2 

4.96 

IO" 3 

I 


mm/hr 

20 

Wavelength X, cm 

30 50 

75 

100 

Distribution 

2A6 

1.52 

IO" 4 

6.49 

10- 5 

2.33 

10 -5 

1.03 

IO -5 

5.85 

10" 6 

A 

4.0 

2.53 

10" 4 

1.08 

10“ 4 

3.88 

10 -5 

1.72 

10 -5 

9.75 

IO" 6 

C 

6.0 

3.02 

10" 4 

1.25 

10- 4 

4.34 

IO -5 

1.93 

IO -5 

1.09 

IO” 5 

D 

15.2 

7.85 

10- 4 

2.95 

10- 4 

9.23 

10" 5 

4.15 

10 -5 

2.35 

IO" 5 

E 

18.7 

9.09 

10- 4 

3.60 

10- 4 

1.20 

10- 4 

5.36 

10 3 

3.03 

10-3 

F 

22.6 

1.17 

IO" 3 

4.81 

10- 4 

1.66 

10- 4 

7.41 

10 -5 

4.19 

10-3 

G 

34.3 

1.75 

IO" 3 

6.83 

10~ 4 

2.24 

10- 4 

9.95 

10" 5 

5.63 

10-3 

H 

43.1 

2.29 

IO" 3 

8.71 

IO -4 

2.78 

10" 4 

1.23 

10~ 4 

6.98 

10-3 

I 


the amplitudes a n and b n are too complicated to be 
reproduced here. Their numerical evaluation for 
spherical drops of given size and temperature is 



Figure 3. Attenuation in rains of known drop-size dis¬ 
tribution as a function of the wavelength X in centi¬ 
meters. The ordinate scale gives logio a, where the 
attenuation constant a is expressed in decibels per 
kilometer. The letters on the curves refer to the drop 
size distributions given in Table 11. 


quite laborious except for small values of the para¬ 
meter 7 vD/\. They involve Bessel and Hankel func¬ 
tion^ of half-integer order of the parameter ttD/\. 

A series of experimental results are given in Table 
13. These results are to be regarded as maximum 
attenuation values. 

If these results are compared with those of Table 
10 and Figure 2 one sees that, in view of the uncer¬ 
tainty in the temperature of the raindrops and their 
size distribution, the agreement between theoretical 

Table 12 


Rate of Correction factor 0 ( T) 


precipitation, X, 

mm/hr cm 

T = 

0 C 

T = 

10 C 

T = 
18 C 

T = 

30 C 

T = 
40 C 

0.25 

0.5 

0.85 

0.95 

1.0 

1.02 

0.99 


1.25 

0.95 

1.0 

1.0 

0.90 

0.81 


3.2 

1.21 

1.10 

1.0 

0.79 

0.55 


10.0 

2.01 

1.40 

1.0 

0.70 

0.59 

2.5 

0.5 

0.87 

0.95 

1.0 

1.03 

1.01 


1.25 

0.85 

0.99 

1.0 

0.92 

0.80 


3.2 

0.82 

1.01 

1.0 

0.82 

0.64 


10.0 

2.02 

J.40 

1.0 

0.70 

0.59 

12.5 

0.5 

0.90 

0.96 

1.0 

1.02 

1.00 


1.25 

0.83 

0.96 

1.0 

0.93 

0.81 


3.2 

0.64 

0.88 

1.0 

0.90 

0.70 


10.0 

2.03 

1.40 

1.0 

0.70 

0.59 

50 

0.5 

0.94 

0.98 

1.0 

1.01 

1.00 


1.25 

0.84 

0.95 

1.0 

0.95 

0.83 


3.2 

0.62 

0.87 

1.0 

0.99 

0.81 


10.0 

2.01 

1.40 

1.0 

0.70 

0.58 

150 

0.5 

0.96 

0.98 

1.0 

1.01 

1.00 


1.25 

0.86 

0.96 

1.0 

0.97 

0.87 


3.2 

0.66 

0.88 

1.0 

1.03 

0.89 


10.0 

2.00 

1.40 

1.0 

0.70 

0.58 






































































88 


SCATTERING AND ABSORPTION OF MICROWAVES 


Table 13. Experimental values of the maximum 
attenuation per unit precipitation rate. 


X, cm 

(a/p) db per km/mm per hr 

References 

0.62 

0.37 

269 

0.96 

0.15 

256 

1.089 

0.2 

262 


(0.19 

176 

1.25 

< 0.09-0.40 

276 


10.63 

281 

3.2 

0.032-0.042 

261 


and observed values is, on the whole, satisfactory. 
It will be seen that the results reported on K-band 
rain attenuation in Hawaii by the U. S. Navy Radio 
and Sound Laboratory workers 281 are higher than 
those observed by other workers on the same wave¬ 
length. The orographic character of these Hawaiian 
rains which were made up of drops falling about 
300 m instead of ordinary rains falling 1,500 to 
2,000 m may be one of the reasons for this divergent 
result. 

Clouds and Fog 

Observations indicate that fair weather clouds and 
fog are composed of droplets whose diameters do not 
seem to exceed 0.02 cm. Under these conditions the 
attenuation formula takes on a remarkably simple 
form since it becomes independent of the drop size 
distribution. The attenuation formula in this limit 
of very small values of the parameter ttD/\ is 

4.092 mc\ j, 71 

oLab = -^- db/km , (17) 

where m is the mass of liquid water per cubic meter, 
X is the wavelength of the radiation in centimeters, 
and 

6ei /10N 

Cl " (e r + 2) 2 + e« 2 ’ ( 8) 

where e r and e t are the real and imaginary parts of 
the dielectric constant of water at the temperature 
in question and for radiation of wavelength X. Figure 
4 represents the attenuation in clouds and fog in the 
range 0.2 to 10 cm. This graph corresponds to a 


Table 14. Attenuation in decibels per kilometer for ice 
crystal clouds. 


Shape of crystals 

T = - 40 C 

T = 0C 

Spherules 

0.00044 m/X 

0.0035 m/X 

Needles 

0.00062 m/X 

0.0050 m/X 

Disks 

0.00087 m/X 

0.0070 m/X 



Figure 4. Attenuation factor in liquid clouds and fogs. 
T = 18 C. 


liquid water concentration of 1 g per cu m, which 
is undoubtedly rather high. Actually, the observa¬ 
tions indicate that the liquid water concentrations 
in clouds and fog rarely exceed 0.6 g per cu m. 

To this may be added the Table 14 for attenuation 
by ice clouds. In ice clouds m will rarely exceed 0.5 
and will often be less than 0.1 g per cu m. 

Scattering (Echo) 

If we denote by g(j) the back-scattering cross 
section per unit solid angle of a spherical water drop 
and if there is a distribution ni, U 2 , * * * , n k , • • • , n n 
drops per cubic meter, the cloud or rain cross section 
for scattering is 

S(t) = ^ n<<7f(7r)AF (19) 

where AV is the scattering volume of the cloud, on 
the assumption of incoherent scattering on account 
of the random character of the drop distribution. 
The summation includes all the drop groups. The 


































ABSORPTION AND SCATTERING BY CLOUDS, FOG, RAIN, HAIL, AND SNOW 


89 


rain front is usually wider than the irradiated area 
so that the radar beam intersects it. Under these 
conditions, taking AV approximately as a spherical 
shell of thickness Ad, at a distance d from the radar 
set, and denoting by 2 0 the half-power beam width 
of the radar beam, one gets 

AV = 2tt d 2 (1 — cos 0) Ad . (20) 

The rain echo cross section is then 

S(t) = 2nd 2 (1 — cos d)(^Ad n^i (x)^ . (21) 

Remembering that <q(x) or S(tt) is precisely the cross 
section per unit solid angle in the direction of the 
radar set, one gets instead of equation (6) for the 
ratio of received to transmitted power 

for small angles 0 which must be given in radians. 


Table 15. Fraction of incident power scattered back¬ 
ward by a layer of 1 km of rain in different types of rain. 
(Decibels) 


Drop size 









distri- 

V, 


Wavelength in centimeters 



bution* mm/hr 

3 

5 

8 

10 

15 

20 

30 

50 

A 

2.46 

-45 

-54 

-61 

-65 

-72 

-77 - 

-84 

-93 

D 

6.0 

-38 

-46 

-54 

-58 

-65 

-69 - 

-76 

-85 

E 

15.2 

-32 

-37 

-45 

-48 

-55 

-61 - 

-68 

-77 

H 

34.3 

-29 

-35 

-42 

-46 

-53 

-58 - 

-65 

-74 

I 

43.1 

-27 

-33 

-40 

-44 

-51 

-56 - 

-63 

-71 


*See Table 11 for drop size distributions. 


The quantity [Ad2} < n f o , < (ir)] or its value in decibels for 
known drop size distributions has been tabulated in 
Table 15. With this table and the known characteris¬ 
tics of a radar set the ratio P 1 /P 2 can be computed 
at once. In the table Ad is taken as 1 km. Since the 
maximum thickness Ad cannot exceed the pulse 
length, the values found in the table can be adapted 
immediately to any pulse length l by adding to it 
(10 logio l), l being expressed in kilometers. Using 
equation (22) for particular radar sets it is found 
that the theoretically computed echo powers from 
rains agree well with the observed values, if the 
uncertainties of the meteorological knowledge of the 
echoing elements, which are mostly rains and storm 
clouds, is kept in mind. As expected, the echoing 
power of snow is very much less than that of rain. 
The systematic observations on S band by the 


Canadian group 402,422 and on X band by Bent 424 
clearly indicate that precipitation either in the form 
of rain or snow is necessary to produce an echo on 
the scope of the radar set. 

Absorption by the Atmospheric Gases 

It was predicted that oxygen and water vapor will 
absorb electromagnetic waves in the microwave 
range. 259,275 In particular, oxygen was predicted as 
having a resonance band around 5 mm and one line 
at 2.5 mm, while the water vapor absorption is caused 
mainly by a single rotational line of relatively small 
strength around 1 cm. Experiments have confirmed 
both these absorption effects. 272,273 In Figure 5, the 



FREQUENCY IN 10 s MC 


X V.o WT V. 

A IN CM 

Figure 5. (1) Absorption due to water vapor in an atmos¬ 
phere at 76-cm pressure containing 1 per cent water 
molecules, or 7.5 g per cu m. The water resonance line is 
assumed to be at 24,000 me, and its half width at half 
maximum (line breadth) is 3,000 me. (2) Absorption 
due to oxygen in an atmosphere at 76-cm pressure whose 
resonance band at 60.10 3 me is supposed to have a line 
breadth of 600 me. 




































90 


SCATTERING AND ABSORPTION OF MICROWAVES 


individual oxygen and water vapor attenuation 
curves have been plotted in the 0.2- to 10-cm wave¬ 
length range. Any change in the water vapor content 
from the one adopted for this graph (7.5 g per cu m 
or 6.5 g per kg of air) or the total pressure can be 
taken into account in computing the combined 
oxygen and water vapor attenuations, since these 



150 9 0 50 30 24 15 10 6.0 3.0 1.5 1.0 0.6 0.3 

*4-FREQUENCY IN I0 3 MC 


m—i - 1 —n—i—i— r~ m—n—i—i i 

0.2 0.3 0.7 1.25 2 3 5 7 10 15 20 30 50 100 

A IN CM -► 

Figure 6. Atmospheric one-way attenuation. (1) Oxy¬ 
gen and water vapor (total for p = 76 cm Hg, T = 20 C, 
water vapor. = 7.5 g per cu m). (Van Vleck.) (2) Moder¬ 
ate rain (6 mm per hr) of known drop size distribution. 

(3) Heavy rain (22 mm per hr). (4) Rain of cloudburst 
proportion (43 mm per hr). 

are proportional to the partial pressures of oxygen 
and water vapor. For practical purposes the effect 
of temperature variations can be neglected. 

In Figure 6, curve 1, is plotted the total attenua¬ 
tion of oxygen plus water vapor in an atmosphere 


at 76-cm pressure, with the same water vapor content 
as the curve of Figure 5. Curves 2, 3, and 4 are 
additional rain attenuation curves computed for a 
moderate rain of rainfall 6 mm per hr, a heavy rain 
of 22 mm per hr and an excessive rain of 43 mm per 
hr, which is of cloudburst proportions. In any rain 
the result of total attenuation is the sum of the 
oxygen, water vapor, and liquid drop attenuation. 

It is thus seen that for waves of 3 cm or shorter the 
rain attenuation may become prohibitive, whereas 
the gaseous attenuation loses its practical import¬ 
ance at waves longer than about 2 cm. In this 
connection it is to be noted that for millimeter 
waves the rain attenuation begins to level off at 
waves of a few millimeters, as Table 10 indicates, 
and would actually decrease at waves shorter than 
1 mm. However in this range, the water vapor 
absorption due to the strong water lines situated at 
much shorter waves becomes more and more intense, 
and communication or radar on these bands is almost 
totally excluded. It is worth noting in this connection 
that using radiation which is strongly absorbed 
might, in certain cases, be of great operational 
interest. In the oxygen band, for example, short- 
range communication could be achieved without any 
likely interference by the enemy. 

Electromagnetic theory thus gives a satisfactory 
picture of the absorption and scattering phenomena 
of microwaves both by floating or falling water 
drops, or their equivalent in hail and snow, and by 
the oxygen and water vapor of the atmosphere. 

Of the approximately 100 reports which were 
prepared by the Columbia University Wave Propa¬ 
gation Group or were presented at the second, third, 
and fourth conferences on propagation held in 
February 1944, November 1944, and May 1945, 61 
have been selected for publication in the Summary 
Technical Report. Of these, 18 reports, covering 
standard and nonstandard propagation, are published 
in this volume; the remainder are published in 
Volume 2. The reports not included in these two 
volumes were omitted chiefly because their material 
was superseded by later documents. 

The reports in the remainder of this volume appear 
in two sections. Chapters 11 through 15 are concerned 
with standard propagation; Chapters 16 through 27, 
with nonstandard propagation. 















































PART III 


CONFERENCE REPORTS ON STANDARD 
PROPAGATION 






Chapter 11 

A GRAPHICAL METHOD FOR THE DETERMINATION 
OF STANDARD COVERAGE CHARTS a 


T he power density at distance S from a trans¬ 
mitter of unit power depends upon hi and h 2 , 
the heights of the transmitting and receiving anten¬ 
nae, and upon X, the wavelength of the radiation. 
For the high frequencies under discussion, we assume 
the earth to be a perfectly conducting sphere, of 
effective radius r, equal to % that of the earth. We 
are to take into account the so-called divergence 
factor D resulting from the earth’s curvature. 

Even with the simplifying assumptions above, one 
cannot express the power as a simple function of S, 
h h h 2 , and X in a single equation. Accordingly, most 
workers on this problem have introduced various 
arbitrary parameters, as intermediate steps. Differ¬ 
ences in procedure lie primarily in the choice of 
parameters. Whether a method is simple or difficult 
depends upon the character of the parameters. 
Certain procedures suggested are satisfactory for 
determining the number of decibels by which the 
signal is below the adopted standard of 1 /xw per 
square meter, designated here by A; but if we are 
given A, hi, and / and then are asked to compute h 2 
as a function of S, as for a coverage diagram, some 
of the methods become very unwieldy. The present 
method works satisfactorily for either case. 



Figure 1. Geometry for determination of standard cov¬ 
erage. 

In selecting a parameter we have been guided by 
the following conditions. The number of parameters 
should be kept to a minimum; the remaining vari¬ 
ables hi, h 2 , and S should appear in the final equa¬ 
tions, if possible. Also it should be unnecessary to 
interchange transmitter and receiver according to 

a By Lt. Comdr. D. H. Menzel, USNR, Office of the Chief 
of Naval Operations. 


the condition that h 2 is or is not greater than hi 
The arbitrary parameter a is defined as follows. 
Let di be the distance from the transmitter to the 
point at which the ray is reflected and d 0 the distance 
to the point where a ray is tangent. Then 

of = <8(1 - a) = 2hir(l - a) . (1) 

a, therefore, is constant along a reflected ray; a = 0 
corresponds to the continuation of the tangent ray; 
a = % corresponds to a reflected ray perpendicular 
to the mast of the transmitting antenna; a = 1 is 
the vertical ray. Thus 

0 < a < 1 , 

with a > % over a large portion of the range of 
interest for the frequencies involved. 

Equation (1) leads to the following relationship 

s- + -- ~ 2 + y S V&hi + 2 rA, • (1 - 2a) 

(1 — a ) 5 

- 2 rh 2 = 0 , (2) 

an irreducible cubic in a. It is this fact that makes 
the problem mathematically difficult and makes 
impossible the explicit elimination of a. 

Additional equations are 


ir- 


4 — 3a — 4\/2/7*, S 1 (1 — a)® 1 3a 


(3) 


an approximation holding well over the region of 
interest since a > The phase difference «i>, result¬ 
ing from the difference in optical path between the 
reflected and direct rays, is 


47r/?, 2 a 2 |~ 1 l”j 

X LV / 2r/l 1 (1 -a) ~ S] ’ 


(4) 


and for the transmitted power 


10- 4 ' 1 


10 6 1 pi - D) 2 , n • , *1 

= + 2J 


(5) 


Here we have four equations. If hi, X, and A are 
specified, there remain five unknowns: D, <f>, a, h 2 , 
and S. Thus we should be able theoretically to elimi- 


93 










94 


DETERMINATION OF STANDARD COVERAGE CHARTS 


nate all but h 2 and S, defining our coverage diagram. 

We may substitute the approximate value for D 
into equation (5) and also use equation (4) to elimi¬ 
nate S from the equation 


equation (2), to determine h 2 . This equation can also 
be thrown into nomographic form if we set 

- h* = h't ( 8 ) 



We may now set 



which correspond to the maxima of the lobes. We 
may alternatively take 

4 > = tit , (7b) 

corresponding to lobe minima or, more generally 

$ = (n + b) tt (7c) 

to represent any specific position on the lobe. 

With A, hi, X#, and a as variables, we may throw 
equation (6) into the form of a nomogram, from 
which we determine a, first for the lobe tips, second 
for the minima, and third for as many intermediate 
points as are necessary. 

With the a’s so determined, proceed to equation 
(4), also in nomographic form, to get S. Finally, use 


where h' 2 is measured vertically from the line tangent 
to the base of the transmitter. 

Another somewhat simpler type of coverage dia¬ 
gram is possible. If we take 


lO-A-no = 


10 6 
47TaS 2 


(9) 


as defining the intensity for a transmitter in free 
space, we get for the ratio of the two 

10 — u - A *)/ 10 = “ 3a 

4 (r^)’ sin2 !’ (10) 

where B is the number of decibels by which the 
actual field exceeds the free space value. Coverage 
diagrams of this type consist of lines radiating from 
the transmitter, rather than contours. For non¬ 
standard propagation the drawings have some com¬ 
plications, but the procedures are clear. This method 
has the additional advantage of fitting in with the 
theory used for surface targets, for which it is simpler 
to use free space intensities and lump the field 
strength integrated over the target area as an 
“effective” target area in a uniform field. 













Chapter 12 

NOMOGRAPHIC SOLUTIONS FOR THE STANDARD CASE 


T he equations given in the preceding chapter 
have now been thrown into nomographic form. 
When these nomograms are employed a rapid method 
for constructing coverage diagrams results. 

Let hi denote the height of the transmitter in 
feet, / mc be the frequency in megacycles, n be an 
integer (1, 2, 3, • • •) specifying the number of the 
lobe, h(0 ^ b < 1) a “phase” factor specifying the 
position on the lobe, and r the radius of the earth. 
Introduce the quantity B defined as follows. 

D 150 (n - h) V2N (3.281)1 

B 1 i/. 

hl 2 f me 


= 3.676 X 


10 6 (n - b) 
hirfmc 


( 1 ) 


where we have taken r = 8.50 X 10 6 m, as the 
approximate % earth value. We have to decide on 
the interval for h. By taking b = 0, %, %, %, %, %, 
we actually obtain seven points on each lobe, 
which should be sufficient for the purpose of drawing 
a coverage diagram. Hence, n — b = 0, %, }{, y 2 , 
%, %, 1, Ye, * * *, etc., spaced at intervals of %. 

Equation (1) is represented in the nomogram of 
Figure 1. We are given hi and / mc , the height and 
frequency of the transmitter. Connect the appro¬ 
priate values on the scales by a straight line and 
mark the point of intersection on the central vertical 
line. 

Define a quantity k by the equation 



so that k = 3 corresponds to the maximum of the 
first lobe, k = 6 to the minimum, k = 9 to the next 
maximum, k = 12 to the minimum, etc. k = 15, 21, 
and 27 correspond to the third, fourth, and fifth 
maxima, respectively. Other values of k determine 
intermediate points on the lobe. 

Now draw a straight line from k = 1 through the 
point previously determined on the central vertical 
line until it intersects the left-hand axis of B. Read 
off B or 1/B, whichever is given. Repeat the process 
for k = 2, 3, • • •, etc., until a value of B is obtained 

a By Lt. Comdr. D. H. Menzel and Lt. A. L. Whiteman, Office 
of the Chief of Naval Operations. 


that exceeds 10; in other words, continue until the 
straight line runs off the lower edge of the left-hand 
scale. 

There will be cases, however, usually involving 
large values of hi or / mc , where B will still be small 
(1/B large) even for k = 27. When this condition 
exists, the lobes tend to be so closely spaced that 
the individual maxima are difficult to define and 
even more difficult to draw on a coverage chart. 
For such conditions an alternative procedure is 
recommended, which will be given later. 

If no difficulty is encountered, however, enter the 
values of B or 1/B (designate the latter with an 
asterisk) in a table such as Table 1. 

Table 1 


/me = Frequency in mc 
hi = Height of antenna in ft 


k = B* 

n 

h 

1 

1 

i 

6 

2 

1 

1 

3 

3 

1 

\ max. 

. 4 

1 

! 

5 

1 

I 

6 

2 

0 min. 

7 

2 

i 

6 

8 

2 

1 

3 

9 

2 

\ max. 

10 

2 

! 

11 

2 

5 

6 

12 

3 

0 min. 

15 

3 

\ max. 

21 

4 

I max. 

27 

5 

\ max. 


*Put an asterisk after an entry if the value read off is equal to l/B. The 
corresponding values of n and b are entered in columns 3 and 4 of the form 
sheet. 


It should be noted that equation (1) is easy to 
solve, and the operator familiar with mathematical 
procedures may prefer to use direct calculation, by 
slide rule or logarithm tables, as much more accu¬ 
rate. In general, however, the nomogram values are 
sufficiently accurate for the work. 

Next, for the five or six assumed values of decibels 
for which contours are desired, we solve a subsidiary 
equation for Y by means of a nomogram (not repro¬ 
duced here). We note that 

Y = db + 60 — 10 log (2rrhi) , 


95 









96 


NOMOGRAPHIC SOLUTIONS FOR THE STANDARD CASE 


h, 



Figure 1 


I llJ II■ iwmul I J _1 LUilmuimi 1—1 1 11 iiu 















NOMOGRAPHIC SOLUTIONS FOR THE STANDARD CASE 


97 


and slide-rule calculation is extremely convenient. 
For each of the selected values of b, we have pre¬ 
pared a nomogram connecting Y, B , and a. Although 
there are six adopted values of b, the expressions for 
b = %, %, % coincide, so that four charts 

suffice. A representative sample of these charts, for 
b = 0 , is given in Figures 2 and 3. Connect each 
value of Y, for which a contour is desired, with the 
value of B on the appropriate chart, according to 
the value of b (or k). Read off the corresponding 
value of a. 

Having determined a for a given point on the 
coverage chart, we now calculate S from the nomo¬ 
gram in Figure 4, with a, db, and S as variables. 
For S measured in units of 1,000 yd, we have 


!()-<»/ 2 ° _ 


10 3 
y/ 7T 





sinV 6 


r 


A typical example for the selected values of b is 
shown, as before. 

Finally, we must calculate /? 2 . For heights we have 


H = /12 (1 — oc)h 1 


(3.281) (914) 2 
2 r 


S ' 2 


. ( 3 . 281) 2 ( 914 ) ( 150 ) (n - b) (- 2 + 3a) c , ON 

"l 1 / 9 O • \^J 

hi fmc 

This equation, unfortunately, has too many variables 
for nomographic solution in a single step. We first 
define a quantity C, such that 

( 3 . 281) 2 ( 914 ) ( 150 ) (/? - ft ) (- 2 + 3 a ) 

hi f m c <*' 2 

Obtain the simple product /?i/ mc , which is a charac¬ 
teristic of the set. Then use the nomogram of Figure 
5 to obtain the values of C for the selected ranges of 
k and a. Then we can determine H from the nomo¬ 
gram of Figure 6, for each value of S and C. Finally, 
from a nomogram (not shown here), representing 
the equation 

; l2 = H — (1 — a)hi 

we determine /i 2 . Actually, for much of the range, 
a ~ 1 and h 2 ^ H. 

For the upper lobes considerable simplification is 
possible. We may omit all the steps involving cal¬ 


culation of a. We determine the various B ’s as before. 
Then, as long as B » 1 we employ the equation 

10 """ - V (srs)’* 

\_7i' 1 f 1 ~ Ji ) sln ' T ' J ] 

This equation gives S directly for each decibel value 
and assumed value of 6 . The nomogram for this 
problem appears in Figure 7. We then obtain H from 
equation ( 2 ), with a set equal to unity. 

H = (3.281) (914) 2 S2 
2 r 

+ (3.281) 2 (914) (150) s . (3) 

C 

In equation (3) we have written C' instead of C. 
For much of the range, wherever B is very large, 
we may take C ~ C. If greater accuracy is desired, 
we may compute C f directly by the equation 

_ (3.281) 2 (914) (150) k / _ J_\ 

6 /me ^1 V B*)' 


It is interesting to note that equation (3), apart 
from the correction factor (1 — 1 /B 2 ), which merely 
serves to improve the accuracy of the result, is 
familiar to many in the construction of so-called 
“fade charts.” These diagrams depict merely the 
lobe minima (and sometimes also the maxima). If 
we set b = 0 we get the former, and if we take 
5 = 1 ^ we determine the latter. 

The total number of lobes N is approximately 



hi /me _ 

(150) (3.281) 


= 2.03 X 10" 3 /ii/ mc 


for hi in feet. These will be distributed over an angle 
of 90 degrees. Hence A, the average angle per lobe, is 


- 90° 4°43 X 10 4 

A ~~ N f mc hi 


Near the horizon, however, the angle per lobe A 0 is 
somewhat smaller, to wit: 

360° 5°64 X 10 4 

A ° “ tN ~ fmc hi * 

















98 


NOMOGRAPHIC SOLUTIONS FOR THE STANDARD CASE 



Figure 2 







NOMOGRAPHIC SOLUTIONS FOR THE STANDARD CASE 


99 



1.9 


L7 


1.6 


US 


L4 


1.1 


1.0 


.9 


.0 


.7 


.5 


.4 


.3 


.2 


Figure 3 







100 


NOMOGRAPHIC SOLUTIONS FOR THE STANDARD CASE 


DB 


00 


' 75 


70 


-65 


-60 


-55 


-50 


45 


40 


35 


30 


- 25 


S 

^ - 300 
g-250 
EE- 200 

1^150 
jp-125 
=-100 
-75 

- 50 

— 25 
EE— 20 

=-15 
-10 


! 

T 


.8- 

. 6 - 

.4- 

.2- 


-.2 


-.2 

-A 
=-.f 

-.7 


-.8 *>=° 


-.95 


EXAMPLE SHOWN BY DASHED LINE 
b= 0 
(X=.3 
D B= 57 
S= 150 

S IN THOUSANDS OF YARDS 


-.99 


20 


Figure 4 














c 

=2 1000000 

5- 500000 
—- 400000 
- 300000 

— 200000 

~ 100000 

50 000 
40000 
30000 

20000 

10000 

5 000 
4000 
3000 *' 

=- 2 000 

=- 1000 

500 
— 400 

- 300 




NOMOGRAPHIC SOLUTIONS FOR THE STANDARD CASE 


101 


h,fme 


oc 

— .01 


2 000000 


1000000 — 


WHEN 0t> 2/3, C IS POSITIVE 
h, IN FEET;f mc IN MEGACYCLES 


500 000 


100 000 — 


— .04 

— .05 



50 000 


10 000 


5000 


1000 


500 


200 

• 

':S8 

>WN BY DASHED LINES 

.80 

k = 3 

.75 

a = 0.48 


mc = 100,000 

.70 

C =-18 

.69 

< 2/3, C IS NEGATIVE 

.66 


.67 


.02 


.03 


.10 


.20 

.25 

.30 

.35 

40 

.45 

.50 

.55 

.60 


— .65 


— .66 


Figure 5 














102 


NOMOGRAPHIC SOLUTIONS FOR THE STANDARD CASE 


420 


1 


♦ 18 - 


♦>« — 

-H4- 


-H2- 


—4 


•HO —H.-.-. 

+8- 

♦6 - 

EXAMPLE SHOWN BY DASHED LINE 
S = 220 
C =+ 10 
H =10,000 
H IN FEET 

S IN THOUSANDS OF YARDS 

- 4 - 


- 8 - 

-‘o-d 

=1 

- 12 - 

- 14- 

- 16- 

-18 - 

- 20 —* 




Jo 0 


Figure 6 












NOMOGRAPHIC SOLUTIONS FOR THE STANDARD CASE 


103 





e 


b = o 
1.0 


b * Vi 


— 1.2 


1.3 



E- 4.5 


5.0 


EXAMPLES SHOWN BY DASHED LINES 

b = 0 b = V 6 

B = 3.75 4 = B = 10 

S = 70 S = 7 
DB = 64 DB = 27 



5.5 


- 6.0 


6.5 


— 7.0 


— 7.5 


E- 0.0 


8.5 


0 


Figure 7 


9.0 

9.5 

10.0 











104 


NOMOGRAPHIC SOLUTIONS FOR THE STANDARD CASE 


HEIGHT IN FT COVERAGE CHART 



Figure 8 


Table 2. Work sheet for coverage diagram calculations, 
db = 46 (MIT - 95 db) 

' mc = 3,000 Y = 13.9 




II 

h- 1 

O 

o 

r+- 



hif me — 

300,000 



k 

B 

n 

b 

O' 

S 

C 

H 

h 2 

1 

0.21 

1 

i 

6 

0.478 

53.5 

-2.15 

350 

300 

2 

0.42 

1 

1 

3 

0.581 

82.5 

-1.29 

950 

908 

3 

0.63 

1 

1 

S 

0.655 

93.0 

- .20 

1,350 

1,316 

4 

0.84 

1 

3 

3 

0.72 

85.0 

1.07 

1,250 

1,222 

5 

1.02 

1 

5 

6 

0.778 

52.5 

2.45 

600 

568 

6 

1.22 

2 

0 



• 



7 

1.35 

2 

1 

6 

0.828 

56.0 

4.10 

750 

733 

8 

1.55 

2 

1 

3 

0.835 

94.0 

4.70 

1,850 

1,834 

9 

1.85 

2 

1 

2 

0.863 

109.0 

5.70 

2,550 

2,536 

10 

1.95 

2 

2 

3 

0.873 

98.0 

6.60 

2,200 

2,187 

11 

2.1 

2 

| 

0.893 

57.0 

7.80 

950 

939 

12 

2.3 

3 

0 






15 

2.9 

3 

1 

2 

0.923 

114.0 

10.80 

3,300 

3,292 

21 

3.9 

4 

1 

2 

0.951 

118.0 

15.40 

4,100 

4,095 

27 

5.3 

5 

1 

2 


119.0 

23.5 

5,100 

5,100 
















































































































































NOMOGRAPHIC SOLUTIONS FOR THE STANDARD CASE 


105 


When A 0 < 0°.l, the lower lobes are so closely 
packed that the drawing of a coverage diagram 
becomes almost impossible. For such cases one 
should determine, for a given decibel value, the lower 
edge of the lowest lobe. Then, with the aid of the 
nomograms for 6 = y 2 , calculate merely the posi¬ 
tions of maxima of the other lobes. 

A work sheet for coverage diagram calculations 
is shown in Table 2. As an illustrative example we 
have selected the case in which 

hi = 100 ft, / mc = 3,000 me, db = 46 . 

Here db stands for the number of decibels that the 
power density is below standard, where we have 
assumed a power of 1 w for the transmitter. The 
symbol db is defined differently by the MIT group. 
The correspondence is: 


db y — [c^&mit + 49] . 

The value of X, which depends only on db and hi, 
was obtained from the nomogram of Figure 4 and 
equals 13.9. The product hif mc is, of course, 300,000. 
The rest of the table was filled out by the methods 
just described. 

The lobes corresponding to this data were also 
computed by the MIT method and are shown 
plotted in dotted lines in Figure 8. In general, these 
lobes agree completely with our own. In the cases 
where there is some slight variance, we have also 
drawn our lobes in heavy lines. Note that the MIT 
db of 95 corresponds to our db of 46. The nomograms 
presented herein correspond to a reflection coefficient 
of —1. For any other value they would have to be 
redrawn. 




Chapter 13 

THEORETICAL ANALYSIS OF ERRORS IN RADAR 
DUE TO ATMOSPHERIC REFRACTION 1 


131 PURPOSE 

T his report is a theoretical evaluation of errors 
in altitude, azimuth, and range caused by atmos¬ 
pheric refraction. These errors are compared with 
the error tolerance specified in military characteris¬ 
tics for fire control radar equipment. Regional 
climatological data are utilized to determine probable 
refractive index gradients used in the determination 
of the error. Errors in heightfinding resulting from 
ducts are also treated. An Evans Signal Laboratory 
[ESL] report now under preparation discusses errors 
which may occur during specific meteorological 
situations and which may exceed the errors indicated 
in this report. 

132 PROCEDURE 

The variation of the index of refraction perpen¬ 
dicular to the path of a radio wave results in a 
curvature of the ray toward the higher index. The 
curvature of the ray is approximately equal to the 
rate of decrease of the index of refraction with 
altitude. Errors due to atmospheric refraction will 
therefore depend on the rate of decrease of the 
index of refraction perpendicular to the ray path 
and to the range. A simplified equation for the error 
in azimuth and altitude is derived below and is 
utilized in this report. This method has been found 
to check to within a thousandth of a degree with 
more accurate methods b of ray tracing. 6 

The rate of decrease of the index of refraction in 
a standard atmosphere is 12 X 10 -6 unit per 1,000 
ft up to 4,000 ft above mean sea level. This corres¬ 
ponds to a curvature of the path of the ray approxi¬ 
mately one fourth the curvature of the earth. The 
standard atmosphere represents average conditions 
in temperate zones. In tropical air such as exists in 
equatorial regions and southeast Asia and southeast 

a By Raymond Wexler, Signal Corps Ground Signal Agency. 
b Errors in angle of altitude due to a duct with a standard 
atmosphere above the duct have been computed by members 
of Group 42 of the Radiation Laboratory. Values computed by 
the method outlined below under Derivation of Formulas 
have been found to agree with their results. 

c For a more detailed analysis of ray tracing methods, see 
reference 75. 


United States in summer, the average rate of decrease 
of the index of refraction is approximately 18 X 10 -6 
unit per 1,000 ft up to 6,000 ft corresponding to a 
curvature of the ray % that of the earth. Over trade 
wind regions of the ocean (latitude 10° to 30°) dry 
subsiding air exists over a moist tropical layer. The 
rate of decrease of the index of refraction in these 
regions is approximately 24 X 10 -6 unit per 1,000 ft 
corresponding to a curvature of the ray one-half that 
of the earth. Within layers of atmosphere designated 
as “ducts” the curvature of the ray may exceed the 
earth’s curvature and may result in a trapping of the 
ray within the duct. Errors due to atmospheric 
conditions in each of the above atmospheres are 
analyzed. In Table 1 are tabulated values of the 
index of refraction at selected levels for the standard 
atmosphere, tropical atmosphere, and tropical dry 
atmosphere as utilized in this report. 


Table 1 . Values of the index of refraction for selected 
levels in different air masses.* 

(n — 1) 10 6 ; n = index of refraction. 


Elevation above 
mean sea level 
(feet) 

Standard 

atmosphere 

Tropical 

atmosphere 

Tropical air 
dry air above 

0 

324 

394 

348 

2,000 

300 

358 

300 

4,000 

276 

322 

260 

6,000 

255 

286 

242 

8,000 

236 

255 

227 

10,000 

219 

234 

216 

15,000 

191 

195 

179 

20,000 

151 

159 

146 

30,000 

105 

107 

105 


*Aerological data for Miami and San Diego for July 1943 were utilized to 
compute the indices of refraction for the tropical atmosphere and the trop¬ 
ical atmosphere with dry air above, respectively. 


133 APPLICATION TO GROUND 
RADAR EQUIPMENTS 

Gunlaying (Antiaircraft) Radar 

Military characteristics for gunlaying radar call 
for a tolerance of 50-yd error in a range of 29,000 
yd and an angle of 1.5 mils in azimuth and elevation. 
Initial angles of sight are between 10° and 90°. 
Results 

In a standard atmosphere, errors in angle of eleva- 


106 







APPLICATION TO GROUND RADAR EQUIPMENTS 


107 



A 


TRUE 

EARTH 

APPARENT 

l-RUE ALTM 

HORIZON P 

ALTITUDE 

'UDE 

LANE 




• 

TROPICAL 

ATMOSPHEI 

RE DRY AIR. 

-AB0VE-*y 

/ 

TROPICAL 

ATMOSPHI 






0 25 50 75 100 

RANGE IN MILES 

B 


Figure 1. Maximum errors in absolute altitude due to atmospheric refraction. A. True earth radius. B. 4/3 earth 
radius. Target assumed to be at true angle of zero degrees. 


tion for a range of 29,000 yd and an initial angle of 
sight 10° are 0.5 mil. A maximum error is obtained 
at 0.9 mil. For an initial angle of sight of 20° the 
maximum error is about 0.6 mil as compared to an 
error in a standard atmosphere of 0.4 mil. Errors in 
azimuth and range are negligible. 

Early Warning Heightfinding Radar 

Military characteristics call for the following 
tolerances in heightfinding radars. 


Set 

Freq. Band Accuracy Required 

AN/CPS-4 

S 

1,000 ft in absolute altitude and 
500 ft in relative altitude at 45 
miles range, preferably 90 miles. 

AN/CPS-6 

S 

1,000 ft in absolute altitude and 
500 ft in relative altitude at 75 
miles range, preferably 100 miles. 

AN/TPS-10 

X 

• 

1,500 ft in absolute altitude and 
500 ft in relative altitude at 50 
miles range. 


Absolute Altitude 

Figure 1A indicates the errors in absolute altitude 
for different air masses on the assumption that the 
target is at a true angle of zero degrees. Thus at a 
range of 75 miles the error in elevation is 940 ft in 
a standard atmosphere and 1,880 ft in a tropical 
atmosphere with dry air above. Figure IB depicts 
the errors on the assumption that the standard 
atmosphere correction (% earth radius) is applied. 
Thus with the % earth radius correction the error 
remains under 1,000 ft at 75 miles. However, these 
atmospheric conditions represent normal conditions 
so that in specific meteorological situations the error 
may exceed 1,000 ft in 75 miles especially in the 
trade wind regions. 

Since the maximum error occurs at a true angle 
of 0°, these errors in absolute altitude for a range of 
75 miles are tabulated for true angles of 0° to 3°. 







































108 


RADAR ERRORS DUE TO ATMOSPHERIC REFRACTION 


Table 2. Errors in absolute altitude for early warning 
heightfinding. Range 75 miles. 

True Angle of sight (degrees) Errors in altitude (feet) 
angle Standard Tropical Standard Tropical 


0 

0.14 

0.20 

941 

1,412 

1 

1.12 

1.17 

823 

1,332 

2 

2.10 

2.14 

705 

970 

3 

3.09 

3.12 

626 

845 


Ducts in the lower layer of the atmosphere will 
cause errors to exceed those specified by military 
characteristics. For a duct depth of 25 ft and 1-unit 
decrease in the modified index of refraction, errors 
in absolute altitude may exceed 1,000 ft within 
ranges of 50 miles. A 200-ft duct, in which the 
modified index of refraction decreases 10 units, may 
cause an error of more than 2,000 ft in 50 miles 
range. Figure 2 depicts errors in absolute altitude 



Figure 2. Maximum errors in absolute altitude due to 
surface ducts with standard atmosphere above. 


for ducts of various depths on the assumption that 
the ray just escapes the top of the duct into a stand¬ 
ard atmosphere above. The rate of decrease of the 
modified index of refraction in the duct is 1 unit 
per 20 ft (corresponding to a curvature of the ray 
about twice that of the earth). 

Relative Altitude 

As an exmple, let us assume that five aircraft are 
located at altitudes of 3,000, 8,000, 13,000, 23,000, 
and 33,000 ft above mean sea level. Suppose that 
these planes are detected by radar at ranges of 50, 
75, and 100 miles. Errors in relative altitude occur 
because of differential refraction at high and low 


levels. Even in a standard atmosphere errors in 
relative altitude arise since the rate of decrease of 
the index of refraction near sea level is 12 X 10 -6 
unit per 1,000 ft, while at 15,000 ft it is only 6 X 10 -6 
unit per 1,000 ft. In a tropical atmosphere with dry 
air aloft the errors are likely to be considerably 
greater since the rate of decrease of the index of 
refraction with height is greater. 


Table 3. Errors in altitude relative to lowest plane 
located at 3,000 ft above mean sea level. 


Separation 
of planes 
(feet) 

Standard 

atmosphere 

(feet) 

Tropical 

atmosphere 

(feet) 

Tropical 

dry 

(feet) 


Range 50 miles 


5,000 

35 

24 

317 

10,000 

73 

107 

380 

20,000 

131 

243 

514 

30,000 

171 

306 

572 


Range 75 miles 


5,000 

78 

54 

713 

10,000 

164 

242 

924 

20,000 

287 

539 

1,158 

30,000 

389 

693 

1,290 


Range 100 miles 


5,000 

139 

97 

1,270 

10,000 

376 

431 

1,644 

20,000 

527 

960 

2,061 

30,000 

673 

1,237 

2,296 


Thus in a tropical atmosphere with dry air aloft 
such as exists in the trade wind areas over the ocean 
errors of some 500 ft relative altitude for planes 
separated by 20,000 ft would occur in a range of 50 
miles. For 100-mile range, errors can be as much as 
2,000 ft. Even in a standard atmosphere errors are 
more than 500 ft for ranges of 100 miles for the 
higher level planes. 

Azimuth and Range 

Errors in azimuth are negligible for all meteoro¬ 
logical conditions except possibly for propagation 
parallel to a sea coast or sharp cold front (see para¬ 
graph below). Errors in range are likewise negligible 
for all possible meteorological conditions. 

Surface Surveillance Radar 

Military characteristics for sets AN/MPG-1 and 
AN/FPG-2 specify errors up to 0.05° in azimuth at 
28,000 yd and 50,000 yd respectively. Range error 
toleration is 20 yd in 50,000 yd. 





















CONCLUSIONS 


109 


Azimuth 

Errors in azimuth arise from horizontal variations 
in the index of refraction in the atmosphere. Generally 
these variations are of insufficient magnitude to cause 
such errors to be appreciable. In order to obtain an 
error of 0.05° in 50,000 yd it can be shown that a 
change in the index of refraction of 1.5 X 10~ 6 unit 
in 44 yd perpendicular to the path of propagation 
is required. This corresponds to an increase of 1C 
temperature and a decrease of 0.1 mb in vapor 
pressure. Such changes within 44 yd may occur in 
propagation parallel to a sea coast or to a sharp 
cold front, or in isolated regions such as between 
forest and meadow, valley and plain, or land and 
water surfaces. Except in the vicinity of a cold front 
or sea coast it is unlikely that such horizontal gradi¬ 
ents of the index of refraction exist along the entire 
path of the ray. 

Range 

Errors in range due to vertical refraction within 
a duct are approximately of the order of 1 yd in 
50,000 yd. The error in range corresponding to an 
azimuth error of 0.05° is estimated at less than 0.2 
yd in 50,000 yd. 


134 CONCLUSIONS 

1. For gunlaying (antiaircraft) radar, the maxi¬ 
mum error in angle of elevation at 29,000-yd range 
is 0.9 mil, as compared to a military tolerance of 
1.5 mil. 

2. In early warning heightfinding radar, errors of 
1,000 ft absolute altitude at 75 miles range may be 
exceeded even with the application of a standard 
atmosphere (% earth radius) correction. Because of 
ducts, errors may be as much as 2,000 ft at 50 miles. 
Errors in relative altitude may likewise exceed 500 
ft in 75 miles. 

3. Errors in azimuth may exceed 0.05° in 50,000 
yd in propagation parallel to a sea coast or a cold 
front. Errors of this magnitude will, however, be rare. 

4. Errors in range are negligible for all possible 
meteorological situations. 

Derivaton of Formulas 

Let the origin of the coordinate system be the 
point where a ray is initially tangent to a line of 
constant index of refraction n 0 , and let the Y axis 


coincide with this line. Since the ray curves toward 
higher index of refraction n, according to Snell’s law: 


n cos (3 = n 0 , 


(1) 


where (3 is the angle the ray makes with the line n. 
Then from trigonometric relations: 


tan (3 = 


dX 

dY 


y/ n 2 — nl 

n Q 


y/n — n 0 y/n + n 0 
n 0 


(2) 


Since n and n Q are extremely close to unity no appre¬ 
ciable error will result if we assume that n -f- n Q = 2, 
hence 


dX 

dY 


V2 

n 0 


y/n — 


n 0 . 


Assuming a linear variation of the index of refraction 
in the X direction, n = n 0 + coX, and 

v n n [ dX y/2X 
y/2u J 0 y/X y/<a 

y2 = 2 ne X 

CO 


Equation (3) indicates that the ray follows a para¬ 
bolic path. Let us convert into polar coordinates by 
the transformation X = r sin 0 and Y = r cos 0, 
where r is the actual range. Then the equation of 
the path becomes 

2 n 0 2 

r = -tan <j> sec <j> . (4) 

CO 

Since in actual practice, </> is extremely small and n 0 
is extremely close to unity, equation (4) can be 
written as 

tan <t> = y . (5) 

Here co represents the rate of change of the index of 
refraction perpendicular to the ray, and 0 is the 
error. If the ray were initially at an angle a to the 
line of equal index of refraction, then the rate of 
change of the index of refraction perpendicular to 
the ray would be co cos a. Hence, more generally, the 
equation for the path of a ray at a mean angle a to 
the lines of index of refraction can be written as 

tan <f> = ^ cos a . (6) 

Equation (6) has been utilized to compute errors in 
azimuth and angle of elevation. 












DIFFRACTION OF RADIO WAVES OVER HILLS 


E xperience has shown that frequencies in the 
VHF (very high frequency) range and higher 
are propagated over hills and behind obstacles more 
easily than has been commonly expected. Hills or 
other obstacles in the transmission path cast shadows 
which may make a radio system unworkable when 
either antenna is located close to the obstacle, but 
recent experiments, notably the work of Jansky and 
Bailey, 334 have shown that hills and mountains can 
cause constructive interference as well as destructive 
interference. In other words, with proper antenna 
siting , the field intensity beyond the line of sight may 
be higher than is expected for the same distance over 
plane earth. This improvement in field intensity may 
be 5 to 10 db or more. 

One attempt to develop a theory for radio trans¬ 
mission over hills is based on the computed field 
intensity over the solid triangle shown in Figure 1. 



Figure 1 . Analysis of field intensity over a solid triangle. 

It was reasoned that a good approximation to the 
field over any profile might be obtained from a 
knowledge of (1) the field over a perfectly smooth 
earth, (2) the field over the solid triangle that 
encloses the actual profile, and (3) the field over a 
knife edge equal in height to the highest point in 
the profile. The theory of propagation over a perfectly 
smooth earth is well known; it is the basis of all the 
published theoretical curves on radio propagation. 
The corresponding expressions for the field intensity 


over a solid triangle and over a knife edge are indi¬ 
cated in a paper by Schelleng, Burrows, and Ferrell, 447 
but some effort is needed to place these expressions 
in a convenient form for computation. 

The method of obtaining an expression for the 
field over a solid triangle is indicated in Figure 1, 
and the same analysis applies to each of the ideal 
profiles shown in Figure 2. The field intensity at any 



Figure 2. Analysis of field intensity over various tri¬ 
angular profiles. 


point P in the vertical plane through the apex of the 
triangle is assumed to be the sum of a direct ray and 
a ray reflected from the ground which is equivalent 
to a ray from an image antenna. In a similar manner 
the field at point P is propagated to the receiving 
antenna by means of a direct ray and a ground 
reflected ray. By integrating over the plane above 
the apex of the triangle (that is, from y — H to 
y — oo and from z — — oo to z = oo) an expression 
for the total received field is obtained. The complete 
expression is not as complicated as the expression 
for propagation over a smooth sphere, but two simple 
approximations will be sufficient for the present 
discussion. When the height of the hill H = 0 and 
when the ground reflection coefficient is —1, the 
complete expression reduces, as it should, to the well- 
known formula for VHF propagation over plane earth. 


E = 2E 0 sin 


2irhih 2 

X (xi + x 2 ) ' 


( 1 ) 


When the height of the triangle H is greater than 
three to five times the average height of the antennas 
and when the reflection coefficient is *— 1, the com¬ 
plete expression reduces to 


417 o 2irHh\ . 2ttH h 2 
E = 4E 0 S sin —-sin —- 


( 2 ) 


“By K. Bullington, Bell Telephone Laboratories. 


\x 


X.T ; 


















DIFFRACTION OF RADIO WAVES OVER HILLS 


111 




The factor S is the shadow loss shown in Figure 3 
as a function of 

.. jj I 2xix 2 

\X (z i + x 2 ) ’ 

The other symbols in the above expressions have 
the following meanings: 

E = field intensity in microvolts per meter, 
E o = free space field intensity in microvolts 
per meter 

= 3 VbP X 10 6 
Xi + x 2 * 

P = radiated power in watts, 

X = wavelength in meters, 

H = height of the obstruction in meters, 
hi,h 2 = antenna heights in meters, 

X\,x 2 = distances as shown in Figure 1 in meters. 

The approximate expression given in equation (2) 
indicates that the field intensity for points well 
beyond the line of sight may be greater than the 
field over a plane earth which is given in equation (1). 
The sine terms in equation (2) indicate interference 
patterns beyond the line of sight which seem to 
offer an explanation for the experimental fact that 
behind hills raising the antenna may cause a loss, 
or lowering the antenna may result in a gain, in 
signal intensity. 

A comparison between theory and experiment is 
shown in Figure 4. These data, which were taken 
from the previously mentioned NDRC report pre¬ 
pared by Jansky and Bailey, show measured values 
at 116 me for horizontally polarized waves propa¬ 
gated over the profile shown in the bottom of the 


Figure 4. Theoretical and experimental results in meas¬ 
uring field intensity of horizontally polarized waves. 

Frequency 116 me. 

drawing. The open circles show the field intensity 
in decibels below the free space value when both 
antennas are 29 ft in height, and the dots give 
similar data for 19-ft antennas. The two dashed 
lines running from upper left to lower right are the 
computed values for smooth earth for 29-ft and 19-ft 
antennas, respectively. The solid line with the inter¬ 
ference fringes is obtained from equation (2) for the 
case of 29-ft antennas. The correlation between 
theory and experiment is not complete, but at least 
the theory may be a step in the right direction. 
Similar theoretical and experimental results are 
obtained with vertical polarization. 

Thus far the only type of profile considered has 
been one with a single prominent hill, and it is 
natural to ask what happens over profiles containing 
several hills. There are less experimental data avail¬ 
able on this point than for propagation over a single 
hill, and consequently the remainder of this discus¬ 
sion is more speculative than the preceding part. 

An ideal profile consisting of two hills of equal 
height is shown in Figure 5. The complete mathe¬ 
matical solution for this case is difficult, but an 
approximation can be obtained in the following 
manner. The field at any point P midway between 
the two hills can be obtained by means of the expres¬ 
sion for the diffraction over a single hill. The field at 
this point is then propagated over the second hill to 
the receiver. The total received field is obtained by 
mechanical integration, that is, by adding the effect 
(magnitude and phase) of many evenly spaced points 
in the vertical plane midway between the two hills. 










































































112 


DIFFRACTION OF RADIO WAVES OVER HILLS 


The net result is that the total received field is 
represented more closely by the path ACB than by 
the path A DEB. The energy received over any given 



/ 

/ 


\ 

\ 

\ 



Figure 5. Field intensity computation for a profile of 
two hills by a solid triangle. 


path such as path ADEB decreases rapidly as the 
number of diffractions in that path increases. How¬ 
ever, for any profile there is always at least one 
path between transmitter and receiver such as path 
ACB that requires no more than one diffraction, 
and the field intensity over this path is usually 
controlling. In other words, the profile consisting of 
two hills can be approximated for computation pur¬ 
poses by a solid triangle which is formed by a line 
from the base of the transmitting antenna to the base 
of the receiving antenna and lines from the base of 
each antenna tangent to the hill that blocks the line 
of sight. By the same reasoning it appears that a 
profile which includes any number of hills can be 
represented approximately by the circumscribing 
triangle. 

The principal assumptions that are basic to this 
method of treating radio propagation over hills and 
other obstructions are as follows: (1) the height of 
antennas is greater than about one-half wavelength, 
(2) the size of obstructions is large compared with 
the wavelength, and (3) the distance between anten¬ 
nas is large compared with either the antenna height 
or the size of the obstructions. These assumptions 


limit the application of this theory to wavelengths 
shorter than a few meters. 

The principal differences between the diffraction 
over an irregular earth and the diffraction over a 
smooth sphere is illustrated in Figure 6 for trans- 



Figure 6. Comparison of diffraction over irregular earth 
and over a smooth sphere for S-band waves over sea 
water. 


mission of S-band waves over sea water. The dashed 
line shows the field intensity versus distance over a 
perfectly smooth earth. The solid line shows diffrac¬ 
tion over a solid triangle which represents what is 
expected when the sea is rough, that is, when the 
height of the water waves is large compared with 
the S-band radio waves. It will be noted that there 
is little difference between the two methods for 
distances less than about twice the optical range, 
but at greater distances the solid triangle theory 
indicates that some energy will be received at 
appropriate distances. 

These views on the transmission of meter and 
centimeter radio waves over multiple obstacles are 
speculative. There is little experimental evidence to 
support them, but also there appears to be even less 
experimental evidence to contradict them. 
























Chapter 15 

SITING AND COVERAGE OF GROUND RADARS 


151 INTRODUCTION 

T his is a general discussion of the effects of terrain 
on the operation of ground radar systems. Written 
to supplement a Signal Corps publication Radar 
Performance Testing , it is intended to provide a 
practical, engineering type of solution of siting 
problems. The principal emphasis is on early warn¬ 
ing and other very high frequency [VHF] systems 
although application may be made to microwave 
and other types of radio equipment. 

The objective has been to enable field personnel 
to compute coverage and other characteristics of a 
given site and radar and reduce the number of test 
flights required to a minimum. Thus the terrain 
factors may be evaluated, and a definite, numerical 
description of the capabilities of a site may be stated. 

Since it is not possible to anticipate all problems 
that may arise in the field, sufficient theory has been 
included to cover a fairly wide scope. In most cases 
several types of solutions are provided so that the 
accuracy and detail required may be related to the 
labor involved. A number of fully worked examples 
are included with a discussion of significant features. 
The drawings are made to scale and to fit practical 
situations. 


152 RADAR SYSTEMS 

15 21 Types of Ground Radar 

Tactical requirements and intensive technical 
development have led to the introduction of numer¬ 
ous types of ground radar equipment. The charac¬ 
teristics and descriptions of these units are given in 
several Service publications. 

Ground radars may be divided into two classes: 
(1) those which utilize ground reflection; (2) those 
which use only the direct ray. Sets which are sited 
so that ground reflection influences their performance 
usually have stringent siting requirements and the 
coverage is dependent on the site. This report is 
concerned chiefly with this type of radar. Equipment 
that uses only direct rays is relatively free from site 

a By Capt. E. J. Emmerling, detailed by Signal Corps to 
the Columbia University Wave Propagation Group. 


restrictions, and the terrain has little effect on the 
coverage. 

1522 Radar Systems—Tactical Aspects 

In most cases radar stations are operated in groups 
for the defense of a region of considerable extent. 
The several stations are assigned sectors in which 
searches are conducted for designated targets, and 
these, when located, are reported to a central agency 
for tactical disposition. Technical operation of such 
groups requires close study of the topography of the 
region so that available equipment and personnel 
may be used to the best advantage. In this way 
adjacent stations may support each other in the 
event of outage due to maintenance or enemy activ¬ 
ity, and other factors may be taken into account, 
such as jamming, atmospheric effects, and perma¬ 
nent echoes. 

The nature of the region to be protected and 
the type of application for which the radar equip¬ 
ment is to be employed are controlling factors 
determining the number, location, and kind of sets 
which must be used. Thus, harbors, islands, and 
inland mountainous regions present problems with 
widely differing operational characteristics. Early 
warning [CHL], fighter control [GCI], gunlaying 
(coast defense), gunlaying (antiaircraft), and search¬ 
light control radars all have different siting require¬ 
ments. This report deals mainly with the first three 
types of equipment listed above, but the methods 
have general application to other problems such as 
the siting of direction finding sets [DF]. 

The early warning radar usually has the mission 
of reporting and identifying enemy aircraft (at say 
20,000 ft) 45 minutes before they can reach the vital 
defense area. This is based on the time required to 
alert the area and to give the defense aircraft time 
to take off and make their attack. Other missions 
may be assigned, such as detection of ships or obser¬ 
vation of friendly aircraft for purposes of control and 
air-sea rescue. Using the moderate plane speed of 
240 miles per hour it is apparent that the early 
warning radar must have a range of 180 miles if 
located near the defense area. Sometimes suitable 
outlying sites, such as islands, are available, and the 


113 



114 


SITING AND COVERAGE OF GROUND RADARS 


coverage may be extended accordingly. The disad¬ 
vantages of outlying sites presented by communica¬ 
tion and supply difficulties, exposure to enemy 
attack, etc., should be carefully considered. More 
often, however, the success of the warning system 
depends on effective long-range operation of radars 
located relatively close to the defense area. The early 
warning stations give periodic reports of the grid 
position of an aircraft and its response to interro¬ 
gation signals. 

The GCI radar is used to direct from the ground 
the operation of friendly fighters against enemy 
aircraft. It has a range of about 50 miles and is 
capable of handling a large volume of traffic. In 
addition to the grid position and identification of 
the target it also determines the height. Surrounding 
the defense area is a region whose width depends on 
the time required to make an interception on an 
incoming enemy plane. The siting objective of the 
GCI stations is the continuous and effective cover¬ 
age of the interception region. Close coordination is 
maintained between early warning and fighter sta¬ 
tions, and the coverage deficiencies of one station are 
counteracted by favorable characteristics of the 
other stations. 

The coast defense gunlaying radar is concerned 
primarily with accurate location of ships. It has a 
range up to 100,000 yd and must be sited fairly high 
and within a few miles of the coast defense guns 
which it directs. This radar supplies accurate data 
on the azimuth and range of the target. 

The antiaircraft gunlaying radar is used primarily 
for directing the guns. Long-range search features 
are usually provided so that they may function also 
as early warning radars, at least to a limited extent. 
They are sited near the guns which are located to 
meet artillery requirements. These units provide a 
continuous flow of data to the gun director giving 
the azimuth, elevation, and range with great accuracy. 

The searchlight control radar is a short-range high 
angle set which is located near the light it directs. 
It furnishes the azimuth, angular elevation, and 
altitude of the target. 

152 3 Radar Siting—Technical Aspects 

In the past some elaborate air warning systems 
have been set up without a competent analysis of 
terrain effects. This resulted in a waste of time and 
money and in failure to adequately provide urgently 
needed radar screens. This failure was caused in 


many cases by the use of prepared coverage diagrams, 
furnished with the equipment, which were computed 
for idealized sites. In mountainous regions where 
only limited reflection areas occur and where the 
sites are very much higher than those used in labora¬ 
tory tests, such diagrams are likely to be very 
misleading. A result of this experience is an unfor¬ 
tunate tendency to explain variations from expected 
coverage by resort to various abstruse speculations, 
with weather not infrequently bearing the brunt 
of the odium. 

It is the purpose of this report to provide an 
engineering type of solution for the bulk of the 
problems that arise in siting and in field computa¬ 
tion of coverage. A more accurate analysis, with 
increased attention to detail, probably is not war¬ 
ranted at this time in view of the relatively rough 
measurements which now are made in the field of 
radar. 

The common early warning radar uses horizontal 
polarization and operates in the VHF band. It must 
be sited from several hundred to several thousand 
feet high in order to obtain sufficiently low angles 
for the range and low coverage desired. Suitable 
sites of the required height may be far inland so 
that an important part of the reflecting surface may 
be rough land or sloping flat areas. Such features 
and also cliff edges, ridges, hills or other obstacles, 
nearby towers and structures will, in general, produce 
a marked effect on the coverage pattern. 

The GCI radar uses horizontal polarization, 
operates in the VHF band and should be sited on 
a large, flat area. The determination of the height 
of an airplane is accomplished by comparing signals 
from two antennas of different heights. If reason¬ 
able accuracy is to be attained the lobe structure in 
the vertical plane must be known with considerable 
precision. Best results are obtained by using a site 
of the extent and flatness prescribed in the instruc¬ 
tion manual. In practice it may be necessary to 
operate on rough ground or limited areas. The ques¬ 
tion may then arise concerning the benefit that will 
be obtained by grading the surrounding areas, or 
how much forest or vegetation should be removed 
for acceptable operation. 

Similar problems arise in siting DF stations. Large 
errors may be introduced by reflection from sloping 
land or other terrain features. 

The effects described above, involving reflection 
from limited areas or rough land or passage of waves 
past an edge, may all be treated as problems of 




TOPOGRAPHY OF SITING 


115 


diffraction, for which solutions are well known or 
may be readily computed. This subject is unfamiliar 
to most Service personnel; but a working knowledge 
of the methods of computation may be obtained by 
anyone who has the usual engineering education. 
Since it is not possible to anticipate all problems 
which may arise in the field, a fairly comprehensive 
discussion of diffraction has been included in this 
report so that even in the absence of other references 
the majority of problems may be treated. 

Other important considerations such as orienta¬ 
tion, visibility, permanent echoes, interference, and 
test methods are discussed. There have been many 
ingenious developments in these subjects in different 
theaters, and where available they have been 
included in this report. Only standard atmosphere 
propagation has been considered. Those who are 
interested in nonstandard propagation should refer 
to the articles on this subject published in this series. 

i5.3 TOPOGRAPHY OF SITING 

1531 Introduction 

The performance of equipment which utilizes radio 
propagation depends upon the character of the inter¬ 
vening land or sea and in particular upon the local 
terrain at the terminals of the propagation path. 
Siting refers to the general problem of selecting and 
utilizing available locations for the best operation 
of the equipment involved. With some types of 
equipment the effects of local conditions are minor, 
and with other types the requirements are most 
exacting. In many cases practical and tactical con¬ 
siderations will compel the use of unfavorable loca¬ 
tions. Performance may then be considerably below 
that obtained in the laboratory or under ideal condi¬ 
tions, and familiar characteristics may be drastically 
modified. 

Field personnel are frequently called upon to 
predict or explain abnormal operation, to devise 
methods of improving poor performance, and to 
make modifications to fit local requirements. This 
discussion will be limited to general principles, and 
reference is made to the instructions furnished with 
the individual equipment for specific details. 

Elements of a communication or radar network 
should ordinarily be viewed as parts of a system and 
not as isolated, self-sufficient units. From this point 
of view a site that gives outstanding results would 
not be satisfactory if it did not help achieve the 


mission of the system. This interrelation between 
various parts of a system, which may extend over 
hundreds of miles, raises numerous problems of 
orientation, visibility, and coverage. 

153 2 Maps and Surveys 

Where available, topographic maps of a scale on 
1 or 2 miles to the inch and contour intervals of not 
more than 100 ft, preferably 20 ft, should be secured. 
Hydrographic charts are valuable in coastal areas. 
If there are no reliable maps, aerial photographs 
may be used to a limited extent. 

Due consideration should be given to the suit¬ 
ability of the map projection for the purposes for 
which it is to be used. The grid system used for 
reporting should be based on the Lambert polyconic 
projection, and not on the Mercator projection. 
Otherwise important errors in azimuth may occur. 
This is especially true at high latitudes. If in coordi¬ 
nating with other services, such as the Navy, it is 
required to use the Mercator projection, the transfer 
from the Lambert projection may be made with a 
transparent overlay of one grid system on the other. 

A transit and a stadia rod are most useful for 
orientation, surveys, profiles, etc. Compasses, clinom¬ 
eters, and other surveying instruments should be 
provided*. In the absence of some of this equipment 
much may be done with improvised devices made 
with plumb bobs and protractors. Rough surveys 
may be made with only a sketching board and by 
pacing off distances. Navigation instruments may be 
used for approximate determination of position. 
Engineer and artillery publications describe orien¬ 
tation methods in detail. Close attention should be 
given to the grid system used for reporting nets so 
that all stations are accurately located. Grid errors 
may be minimized by making all charts from a 
master copy. 

15 3 3 Profiles 

The height of the center of the antenna should be 
determined to within a few per cent. The reference 
level is the main reflecting surface, which is normally 
the sea. Heights given on maps should be checked 
against available bench marks and the terrain. 
Barometers or airplane altimeters are useful for 
height determinations, but their readings should be 
corrected for temperature. 

Where the reflection surface is part or all land, a 



116 


SITING AND COVERAGE OF GROUND RADARS 


profile is usually necessary for estimation of the 
effective antenna height and the reflection charac¬ 
teristics of the terrain. Profiles should be prepared 
of several representative azimuths in the operating 
sector. The accuracy required decreases with the 
distance from the transmitter. In most cases suffi¬ 
cient detail is not available on maps so that a 
personal inspection of the terrain should be made 
to become familiar with the nature of the soil and 
the degree of roughness. Special attention should be 
given to ridges, flat areas, bodies of water, distance 
to the shore, hills to the rear, obstacles in the operat¬ 
ing area and at the boundaries. A knowledge of the 
antenna pattern in both the vertical and horizontal 
planes is necessary for judging what parts of the 
terrain should be more closely examined. 

1534 Orientation 

Where long distances and directive beams are 
involved fairly accurate orientation is required. This 
is especially true of the narrow beam, precision type 
radars. Of the many ways of determining the direc¬ 
tion of north, one of the most convenient is observa¬ 
tion of the azimuth of the sun. Care must be taken 
when using compasses because of local attractions 
or inadequate information of the declinations. Star 
observations are capable of good accuracy, but where 
Polaris is not visible they require the same procedure 
as solar shots. Caution must be used in aligning on 
permanent echoes because nonstandard refraction 
may bring in confusing distant echoes, or side lobes 
may give false echoes. In general several methods 
should be used in order to obtain independent checks. 
When an accurate orientation has been obtained 
reference marks should be provided so that the 
azimuth may be readily checked. 

Solar azimuths, correct to the nearest quarter of 
a degree, may be determined from the date, time 
to the nearest minute, and the latitude and longitude 
to the nearest degree. Two methods will be given 
for obtaining the azimuth of the sun: (1) by calcu¬ 
lation, (2) from tables. A third method gives true 
south only. 

The azimuth of the sun may be calculated from 
the formula: 


cos <t> tan 8 — sin <i> cos HA ’ ' 

/3 = bearing of the sun. 

The bearing is east or west of south when <p-8 is 


positive. The bearing is east or west of north when 
$-8 is negative. The bearing is east in the morning 
(/3 will be negative), and west in the afternoon (0 
will be positive). 

HA = hour angle of the sun. 

During the morning hours when the hour angle is 
greater than 12 hours, its value should be subtracted 
from 24 hours for use in the formula. 

4> = latitude of the place of observation. 

8 = declination of the sun at the time of observation. 

The signs of 4> and 8 are important and each is 
positive when north of the equator and negative 
when south. 

The hour angle HA is the local apparent time 
[LAT] minus 12 hours. To convert the observed time 
into LAT the civil time at Greenwich [GCT] must 
be found and combined with the equation of time 
to correct for the apparent irregular motion of the 
sun. This gives Greenwich Apparent Time [GAT] 
which is converted to LAT by allowing for the lon¬ 
gitude. The equation of time and the declination of 
the sun are plotted in Figure 1 for 1945. The annual 
change is small, and these curves may be used for 
radar work without regard to the year. Standard 
time meridians are every 15° east or west of 
Greenwich, each zone corresponding to 1 hour. Care 
should be used to take daylight saving, or other 
changes from standard, into account correctly. 

Example 1. It is desired to compute the azimuth 
of the sun. 


Given: Date March 16 




Time 1345 hours PWT 

Latitude 40° North 
Longitude 118° West 




Solution : 




The hour angle will be determined first: 




Observed time PWT 


13" 

45 m 

Zone difference 

+ 

7" 


Greenwich civil time 


20" 

45 m 

Equation of time (Figure 1) 



- 9 m 

Greenwich apparent time 


20" 

36 TO 

Longitude difference for 118° W 

- 

7" 

52 m 

Local apparent time 


12" 

44 m 

LAT - 12 = HA 

- 

12" 


Hour angle of sun 

+ 

0" 

44 m 

HA in arc (4 OT = 1°) 



4- 11° 

Latitude 4> 



+ 40° 

Declination of sun 8 (Figure 1) 



- 2° 


Substituting in equation (1): 


_ sin 11° _ 

cos 40° tan (—2°) — sin 40° cos 11° 

0.19 

0.766 X (-0.0349) - 0.643 X 0.982 










TOPOGRAPHY OF SITING 


117 


= 0.29 , 

0 = 16°10'. 

Since <I> — 8 is positive, /3 is the bearing from the south. 
The bearing is west of south since /3 is positive (p.m.). The 
azimuth of the sun is 

180° + 16°10' = 196°10'. 

A quicker solution may be obtained from a book 
Azimuths of the Sun, H. O. 71, published by the 
U. S. Navy, Hydrographic Office. The equation of 
time may be obtained from a current copy of The 
American Nautical Almanac, United States Naval 
Observatory, Washington, D. C. 

This method will be illustrated by the data from 
Example 1. The LAT is obtained as before. Between 
September 23 and March 21 the sun is in south 
declination and since the latitude in this case is 
north, the second part of the book labeled “Declina¬ 
tion Contrary Name to Latitude” is used. For 
latitude 40° an interpolation is made between 12:40 
and 12:50 obtaining 164°. The table is marked “the 
angular departure of the sun west of north” for 
readings in the afternoon, and the tabular value is 
therefore subtracted from 360°, giving 196° as the 
azimuth of the sun. It is usually more convenient 


to plot a curve of azimuth against time for the hours 
during which it is expected that the observation will 
be made. Such a curve may be used for several days 
without much error. 

A method that is less convenient but requires no 
calculation is the equal altitude method. This con¬ 
sists in measuring the horizontal angles between the 
sun and a mark, when the sun is at the same altitude 
on both sides of the meridian of the observer. The 
bisector of the horizontal angle between the two 
equal altitude positions of the sun during the obser¬ 
vations is very close to true south, and the azimuth 
of the mark may be determined. 

A horizontal radiation pattern should be obtained 
to determine whether the electrical and mechanical 
axes of the antenna coincide and to discover any 
abnormalities in the main or secondary lobes. Defec¬ 
tive patterns should be corrected by appropriate 
maintenance. 

15.3.5 Visibility Problems 

It is frequently necessary to estimate the effect on 
rays of intervening obstacles or the curvature of the 



1 II 21 31 10 20.2 12 22 I II 21 1 II 21 31 10 20 30 10 20 30 9 19 29 8 18 28 8 18 28 7 17 27,7 17 27 

V - * ‘— y ,v v- v -V- 1 v -y-' N -y--''- y - M -V- v -y-''-v--y- v -r-' 

JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC 


SUN DATA FROM NAUTICAL ALMANAC 1945 

Figure 1 . Sun data from nautical almanac, 1945. 

















































































118 


SITING AND COVERAGE OF GROUND RADARS 


earth, or to compute the distance to the horizon, or 
the amount a ray would have to be diffracted to clear 
an intervening hill. The methods described here 
enable one to solve such problems quickly and 
simply. 

Distance to the Horizon 

The distance d of the horizon on a spherical earth 
as seen by an observer at elevation h is given by the 
well-known formula: 

d = \/t or h = i d2 ’ (2) 

with d in statute miles and h in feet. This expression 
makes no allowance for refraction and is commonly 
used in visual work. 

In radio propagation work the refraction of the 
standard atmosphere is sufficient to increase the 
distance of the “radio horizon” to 

d = \/2h or h = ^ d 2 , (3) 

where d is expressed in statute miles and h in feet. 
This corresponds to the use of an effective radius of 
the earth equal to ka where k is % and a is 3,960 
miles. This value of k will be used throughout this 
report. If it is desired to use other values of k, 
equation (3) may be written as 

7 ISkh , 2d 2 

d = or h= u- 

Points at heights hi and h 2 which are separated by 
the sea or smooth earth are visible from each other 
if the distance between them is less than 

d L = V2hi + V2h 2 . (4) 


Dip and Rise 

Over land, visibility is determined by the profile 
of the path involved. Elevations obtained from map 
contours may be plotted on a profile so as to take 
the effective earth curvature into account, and visi¬ 
bility can then be determined by graphical means. 
However, construction of such profiles on a curved 
datum line is tedious, and it is easier to compute 
the earth curvature and the visibility directly from 
the map by methods given below. 

In Figure 2 is shown the relations between various 
heights on the earth’s surface. In considering the 
reference line (sea level) flat as on a map or ordinary 
profile diagram, use is made of the line H\TH 2 T' 
instead of the curve H 1 HH 2 H'. This will be com¬ 
pensated for by using a fictitious ray path P 1 PP 2 P' 
instead of the line PiQP 2 Q'. The deviation of this 
fictitious path from P 1 QP 2 Q' at P is QP = HT and 
is called the dip. The deviation at P' is Q'P' = H'T f 
and is called the rise. 

In the figure on the left the triangles HH 2 T and 
H\KT are similar and 

TH 2 HT_ 

TK HiT ’ 

or approximately (right-hand figure) 

HT X 2ka = d\d 2 . 

Therefore the dip, 

5,280 X did 2 X 3 _ d x d 2 m 

y 2 X 3,960 X 4 2 

Similarly for the rise 





Figure 2. Relations between various heights on earth’s surface. Dip and rise. 











TOPOGRAPHY OF SITING 


119 


The application of these formulas will be shown by 
a number of examples. 

Example 2. Intervening Obstructions — Graphical 
Solution. In Figure 3 is shown a profile as may be 



Figure 3. Intervening obstruction of radiation between 
two points. 


obtained from a topographical map. It is desired to 
ascertain whether P 2 will receive radiation from Pi 
without being obstructed by the intervening hill P. 

Owing to the curvature of the earth the line marked 
“datum level” is actually curved instead of being 
straight as shown. To compensate for this distortion 
the line of sight of the radar is taken as the parabola 
P\XP 2 (shown dashed) instead of the straight line 
PiQP 2 . If X lies above the top of the intervening 
hill P, the ray is not obstructed. The distance QX 
is from equation (5). 


did 2 _ 20 X 30 
2 2 


300 ft . 


Scaling this distance down from Q, it will be found 
that X lies above P and there is no obstruction to 
the radiation. 

It will be noted that QX is a maximum midway 
between Pi and P 2 . 

d\ + d 2 ^ . (6) 

Where there are several obstructions to be con¬ 
sidered the work may be speeded by drawing a line 
S\S 2 (Figure 4) parallel to PiP 2 at a vertical distance 





Figure 4. Several obstructions of radiation between 
two points. 


below it equal to the maximum dip. Then intervening 
hills which do not rise above S\S 2 will not have to 
be considered, and those that do cut the line may 


be checked for obstruction by equation (5) as before. 

Example 3. Remote Shielding—Graphical Solution. 
It is frequently desired to know from a position as 
Pi what degree of shielding will be obtained from a 
given profile. In Figure 5 the rise Q'X' is computed 



by equation (5). Since P'lies below X' it is shielded 
from Pi and the minimum height of radiation is 
indicated by the dotted lines 


Q'X' 


di'd 2 ' 

2 


90 X 80 
2 


3,600 ft . 


Example If.. Visibility Determined by Computation. 
In many cases it is not necessary to construct profiles, 
as visibility may be determined by a simple compu¬ 
tation. The critical height, h c , which an intervening 
hill must equal or exceed to obstruct the line of 
sight, may be computed from Figure 4. Let the 
height of the line P\P 2 at d\ be h'. Then 

hi - h' = V - h 2 
d\ d 2 

01 ,, _ h\d 2 4- h 2 d\ 

d\ -f ct 2 

But the height h' exceeds h c by the dip (did 2 )/2; 
therefore 

, h\d 2 + h 2 di d\d 2 ,_ v 

K = STTZ - 2 ~' (7) 

For the values given in Figure 4 the critical height 
at di is 

3,000 X 35 + 1,500 X 15 15 X 35 

K ~ 15 + 35 2 

= 2,287.5 ft . 

Since the hill P is 2,300 ft high it will interfere with 
radiation to P 2 . 

Example 5. Remote Shielding — Computation. An 
important problem is illustrated in Figure 5. A trans¬ 
mitter is located at Pi, and it is desired to know if 
the nearby hill P« shields the distant mountainous 
island. The height of the line P\Q' at a distance of 




































120 


SITING AND COVERAGE OF GROUND RADARS 


d\ from Pi is denoted by h' and may be obtained 
from the relation: 

h% - h' hi - h' 
d*’ di' ’ 

g ivin g „ di'h 2 - djhi 

h ~ di f - d 2 f • 


For this case the rise Q'X' due to earth curvature 
must be added to give the elevation X 9 of the line 
of sight. The height of the lowest ray is therefore 


di'hi — d^hi di'di 

di' - di ^ 2 


( 8 ) 


For the values given in Figure 5 

90 X 2,200 - 80 X 2,400 90 X 80 

h ~ 90 - 80 + 2 

= 4,200 ft . 

It is apparent that the hill P f is shielded from Pi 
by the nearby hill P 2 except by diffraction. 



Example 6. Vertical Angles. The slope of the line 
of sight at the near end (Figure 6) is given by 

= h 2 — hi _ d /q\ 

1 5,280d 10,560' 

61 is in radians and is measured from the horizontal 
at hi. The angle with respect to the horizontal at the 
far end is given by 

hi - h 2 _ d 

2 5,280d 10,560' 

Thus for the values shown 


Oi = 
and 


1,500 - 4,000 50 

5,280 X 50 10,560 


— 0.0142 radian , 


0 2 = 0.00474 radian . 


Example 7. Angle of Diffraction. One of the principal 
problems in connection with intervening obstacles is 
the computation of the angle of diffraction. In Figure 
7 the angle of diffraction is 6 d . The line PiP is the 
geometrical shadow line; h c is the height of the 



Figure 7. Angle of diffraction computation. 


direct line PiP 2 at the distance di and is given by 
equation (7). 


h e — H 
~ 5,280di * 


( 10 ) 


For the values shown in Figure 7 


h c 

e d 


4,000 X 30 -I- 1.500 X 20 
20 + 30 


2.700 ft , 


20 X 30 
2 


2,700 - 2,500 
5,280 X 20 


0.00189 radian . 


P 2 is therefore in the illuminated region. Had hi 
been 100 ft instead of 1.500 ft, h c would be 2,140 
ft and 


2.140 - 2.500 
5,280 X 20 


— 0.00341 radian , 


and P 2 would then have been in the shadow region. 


!54 DIFFRACTION OF RADIO WAVES 
Introduction 

Whenever interference effects are important, the 
reflecting surface must be examined to determine to 
what extent the assumption of an ideal plane or 
spherical surface with uniform values for the ground 
constants is valid. This uniformity holds when the 
reflecting surface is the sea; but it is often not true 
over land areas, and especially at the coastline. 
More important deviations from the ideal case are 
roughness of the reflecting surface, such as waves on 
the sea, or irregularities of the land, such as hilly 
or broken terrain. This frequently causes diffuse 
reflection and virtual elimination of useful reinforce¬ 
ment of the direct ray. To deal with these practical 
terrain problems the methods of physical optics are 
employed. 





























DIFFRACTION OF RADIO WAVES 


12J 


Wave Propagation 

For most purposes the antenna may be considered 
as a point source of radiation. Near the antenna 
the wavefront (the locus of points of constant transit 
time) is spherical, but at great distances it is prac¬ 
tically plane. According to Huyghens’ principle each 
point of a wavefront may be considered as a source 
emitting wavelets whose envelope at a given time 
is the new wavefront. In Figure 8A, 0 is the source 



Figure 8. Radiation wavefronts. A. Spherical wave- 
front. B. Plane wavefront. 


of radiation, and AB a portion of the spherical 
wavefront. From centers a, b, and c, secondary waves 
spread out as shown by the dotted lines and are 
enveloped in the new front A'B'. A similar construc¬ 
tion is made in Figure 8B for a plane wavefront. 

Another example showing how waves are reflected 
from a plane surface is given in Figure 9. A wavefront 
AB is descending in an oblique direction on the 
reflecting surface AB'. Points AC DEB' are struck 
successively and in turn become centers of new 
wavelets. In the time required for B to reach B' 
the wavelet from A spreads to a radius AA', the 
distance it would have traveled if there were no 
reflector. Other wavelets have lesser radii which, in 
spreading, form a new wavefront. This is the reflected 
wavefront, and its angle with the reflecting surface 
is the same as that of the incident wavefront. 

The secondary wavelet from a point on a spherical 
wavefront (AB in Figure 10) does not produce the 
same effect in all directions. The field strength in a 
direction ac varies in proportion to (1 + cos 0). The 
field strength drops from a value 2 in the forward 
direction to 1 along the line xy and to zero in the 
backward direction (0 = 180°). While in Figure 8A 
an envelope of secondary wavelets can also be drawn 



Figure 9. Reflection of waves from a plane surface. 
Huyghens’ construction. 



Figure 10. The secondary wavelet. 


to the right of AB so as to produce a convergent 
wave traveling back to zero, it can be shown that 
this back wave does not exist. Only waves in the 
forward direction should be considered. 


Fresnel Zones 


In Figure 11, BC denotes a plane wavefront 
moving from a distant source on the right toward 








122 


SITING AND COVERAGE OF GROUND RADARS 



a point P to the left. It is desired to know the effect 
at P of the secondary wavelets emanating from the 
wavefront. A straight line is drawn from the distant 
source to point P cutting the wavefront at C. In the 
wavefront with Casa center are drawn circles such 
that the first is a half wavelength further from P than 
C is, the second is 2 half wavelengths, etc., so that 
the secondary disturbance from any circle will reach 
P half a wavelength ahead of those from the circle 
enclosing it. 

If PC = b, the radius n of the first zone may be 
obtained from 

( b + |) 2 - 6 2 = n 2 . 

Neglecting A 2 /4, the radius ri = y/o\ and the 
radii, r 2 = r 3 = \/Sb\, etc., and in general 

r m = y/mb\ . ( 11 ) 


is 7 r 6 A, and each succeeding ring or zone is slightly 
greater. 

The effect which one of the zones produces at P 
is proportional to its area and inversely proportional 
to its distance from P. These factors compensate as 
the radius increases, so that the successive zones 
may be regarded as producing equal and opposite 
effects at the point P. The zones become less effective 
further from the center owing to the increased 
obliquity, since the effect at P is proportional to 
1 + cos 0 (see Figure 10). The resultant effect may 
be represented by a series of terms of alternate sign 
which decrease slowly at first and then more rapidly, 
eventually becoming zero, thus: 

S = mi — m2 T" ^ 3 , etc., 

1 . (I ,1 

= -mi + ( 2 Wl “ m 2 + 2™ 3 


The corresponding areas are approximately ir 6 A, 
2irb\, SirbX, and mirb\. The area of the central zone 


+ 


Q — ra 4 + 













DIFFRACTION OF RADIO WAVES 


123 


It can be shown that all terms except the first cancel 
so that 

s = . (12) 

The resultant effect of the entire wavefront is equal 
to one-half of that due to the central zone. 

The secondary wavelets from the central zone 
unite into a disturbance whose phase is midway 
between the center and the rim. This may be shown 
by dividing the first zone into rings such that the 
effect of each ring at the point P is equal in ampli¬ 
tude, and the phases range over half a complete 
period. The electric vectors corresponding to these 
subdivisions may be combined to obtain the resultant 
phase as in Figure 12. The vector for the central 



area of the first zone is AB with succeeding sur¬ 
rounding rings represented by BC, CD, etc. These 
vectors fall along the perimeter of a half circle, as a 
consequence of which the resultant amplitude is 
2/tt times the sum of the amplitudes of the individual 
vectors. The vectors for the second zone are shown 
dotted. 

In Figure 13 is shown the first six half-wave zones 
and the phases relative to the center of the first zone 
are indicated. A set of alternate black and white 
zones as shown at the top is known as a zone plate. 

If a screen is provided which has an aperture of 
the same diameter as the first zone, it will be found 
that the electric intensity of the wave at the point P 
is doubled (m i = 2S) and the power intensity is four 
times as great as for the unobstructed wave. If the 
aperture is increased to include the second zone, the 
intensity at P will be reduced nearly to zero. The 


( 




disturbances from the second zone are out of phase 
with those of the first zone and equal in magnitude 
and therefore cause cancellation. 


1544 Reflection from Rough Surfaces— 
Rayleigh’s Criterion 

A rough surface may destroy all phase relations 
between the elements on the wavefront. The second¬ 
ary wavelets start from the elevated portions of the 
surface first, since these portions are struck first by 
the incident wave, and the lower portions send out 
secondary disturbances at various other times in 
random phase. It is impossible to arrange any zone 
system on such a surface for there are all possible 
phase differences irregularly distributed over the 
reflected wavefront and each point on the surface 
acts as an independent source radiating in all 
directions. 

In Figure 14 is shown a plane surface xy with 
incident rays SB and SA falling on a raised portion 
and a crevice respectively and being reflected to P. 
The path difference is SA + AP — (SB + BP). 
Since BP and AP are practically parallel, the path 
difference may be taken as BA — BK. 


BK = BA • cos 2F . 












124 


SITING AND COVERAGE OF GROUND RADARS 



The path difference 

A = — — - (1 — cos 2^) 
sin ^ 

= 2 H sin * . (13) 

The corresponding difference in phase is 


15,4,5 Diffraction at Obstacles 

The preceding considerations of Fresnel zones in 
a wavefront will now be applied to the problem of 
radio wave diffraction past hills, ridges, or nearby 
objects. These obstacles will be treated as though 
they were straight edges, narrow screens, or rec¬ 
tangular slits. 

In Figure 15 is shown a distant source of radiation 



Figure 15. Interference of waves at an edge. 


$ = 


2ttA 

X 


4 vH 
X 


sin 'f' . 


(14) 


Since the path difference increases as the grazing 
angle increases, the diffusion is greatest when the 
rays are perpendicular. When the angle is small, 
near zero, regular reflection may be obtained. It was 
suggested by Rayleigh to take as an upper limit for 
the grazing angle, giving regular reflection, the value 
corresponding to a phase difference of tt/ 4. By 
equation (14) this angle is given by 


or 


4t tH 


sin 'F 


sin = 


16 H 


(15) 


For a given wavelength and lobe angle the terrain 
at the reflection point may be examined to determine 
the limiting height of the roughness for regular 
reflections. Equation (15) may also be given in a 
more convenient form using the approximation 
sin 4' = 4' radians for small values of 'F: 


H = 


3,520 


(16) 


with H in feet, / in me, and 'F in degrees. Thus for 
100 me regular reflection may be obtained over 
ridges as high as 35 ft for a grazing angle of 1°, but 
for 3,000 me the roughness could not exceed 1 ft 
in height at this angle. 


and a diffracting edge. The illuminated edge is 
considered to send out secondary cylindrical wavelets 
which interfere with the plane waves which are not 
shielded by the edge. The dotted and solid lines are 
spaced a half wavelength apart. In the unshaded 
region the intersection of two dotted or two solid 
lines indicates reinforcement and the intersection of 
a dotted and a solid line indicates cancellation. 
The loci of maxima and minima are parabolas 
along which the relative intensities are practically 
constant. In the shadow region, where only the 
wavelets from the edge are propagated, the relative 
intensity falls off continuously as the angle of 
diffraction is increased, since the angle 0 (see Figure 
10) approaches 90°. 

In Figure 16 is shown the zone system obtained 
because of a diffracting edge with the source of 
radiation at a distance behind the paper and with 
the edge viewed from a screen on which diffraction 
fringes are formed. The observer is within the 
shadow region a distance be, and the zone system 
is largely obscured as indicated by the dotted lines. 
The radiation received at c comes from the exposed 
zones, and its intensity is equal to a series of the 
form mi - W 2 + W 3 • • • , etc., where mi is the 
electric intensity due to the exposed portion of the 
first uncovered zone, etc. The sum of this series is 
a fraction of mi since the outer zones tend to cancel. 
As c is moved to the right, that is, further into the 
shadow, mi will decrease very rapidly without passing 
through maxima and minima. 



























DIFFRACTION OF RADIO WAVES 


125 



Figure 16. Fresnel zones in the shadow region. 



Figure 17. Fresnel zones on the shadow line. 

In Figure 17 the observer is at the geometrical 
edge of the shadow. Only one-half of the wave is 
effective and the electric intensity is reduced to 
one-half, considering the unobstructed wave as unity. 
Outside the edge, Figure 18, at a distance ab the 
electric intensity is that due to the half of the 
wave, plus such portions of the zones between a and 
b that are uncovered. If an even number of zones is 
uncovered there is approximately a minimum of 
radiation received at the line a, that is, the half 



Figure 18. Fresnel zones in the illuminated region. 

wave plus the effect of the two zones, Yi + m x — m 2 , 
for the case shown. If a were moved to the right so 
that slightly less than one zone were uncovered there 
would be a maximum, + m h in which case wi is 
greater than one-half owing to the partial screening 
of the other zones, which, if allowed to operate, 
would reduce the effect due to the right-hand half 
of the central zone. For this reason the fringes 
formed outside the shadow may exceed the electric 
intensity of the unobstructed wave. As a is moved 
to the left, more zones are uncovered, and the 
maxima and minima are spaced approximately 
according to the radii of the zones; that is, the 
distances are proportional to the square roots of 
1 , 2, 3, etc. 

154 6 Fresnel Integrals 

The preceding discussion is approximate and 
provides a qualitative picture of diffraction phenom¬ 
ena. The problem will now be formulated quanti¬ 
tatively by the method of Fresnel. Since the applica¬ 
tions in view all have to do with diffraction by 
straight edges, slits, etc., the theoretical approach 
will be limited to diffraction of cylindrical waves by 
long edges parallel to the axis of the cylinder. The 
diffraction images of the source will then be bright 
bands also parallel to this axis, and the whole prob¬ 
lem may be reduced to the consideration of rays in 
a plane perpendicular to the axis. The fact that in 
the applications to be discussed later the illumina¬ 
tion is due to a point source rather than a line source 
is probably of little importance provided the distance 









126 


SITING AND COVERAGE OF GROUND RADARS 


from the source to the diffracting edge is sufficiently 
large. 

In Figure 19 is shown a cylindrical wavefront A B 


A 



Figure 19. Effect at point P of wavefront AB. 


cosine law to the triangle MSP, which gives at once 
d 2 = (a + b) 2 + a 2 — 2a (a + b) cos ^ , (19) 


or after a simple reduction, using the identity 


cos 


(s/a) 


1 — 2 sin 2 — 
2 a 


then 


d 2 — b 2 _|- 4 a (a + b) sin 2 ~ . 


( 20 ) 


For the present purpose it is sufficient to consider 
the case when angle s/a is so small that powers of 
s/a above the square may be neglected in comparison 
with unity. This means that 


with its axis at the line source S' (say an illuminated 
narrow slit). The secondary wavelets from the 
various line elements ds of the wavefront arrive at 
P with different phases, having traveled different 
distances MP . It is desired to find the resultant 
field strength MP due to wavelets from any given 
finite part of the front. 

Let the electric field strength at a point in the 
wavefront be given by the expression 

E = E 0 sin 27 rft , (17) 

where t is the time, / the frequency, and E 0 the 
amplitude of E. The phase has been adjusted so as 
to make E — 0 when t = 0. 

Consider next the secondary wavelets spreading 
from the front in the direction of P. The field 
intensity at P due to the secondary wavelet emanat¬ 
ing from the line element ds at the point M (see 
Figure 19) is proportional to dsE 0 and is inversely 
proportional to the square root of the distance 
MP = d (since this is a cylindrical wave). Further, 
the field intensity must show a phase retardation 
corresponding to the distance d, that is 2rd/\. Hence 
the field strength of the wavelet at P is given by 
an expression of the form 

dE = kE 0 ds sin (2x/< - ^ ), (18) 

where k is a factor of proportionality which depends 
to some degree on the angle MPM 0 and the distance 
d, but which will be considered constant here, as the 
dependence of the phase on d is of much greater 
importance. To obtain the intensity due to wavelets 
emanating from a finite part of the front, equation 
(18) must be integrated over the corresponding 
region of s. For this purpose we need a relation 
between d and s. This is obtained by applying the 




d = -\lb 2 + 4a (a + b) sin 2 — ~ 6 

, (a + b) . , s t , (a + b) /olN 

+ 2a ___ sln -_^ 6 + _ r _. s2 , ( 21 ) 


or again, on writing 




(a + b) _ 1 
2 \ab S ~ 2 v 


the phase lag 2ird/\ assumes the form 
2ird 2irb tt 9 

T = X + t ■ 


( 22 ) 


(23) 


Using equations (22) and (23), expanding the sine 
expression of equation (18), it follows that 


dE 


= k 4 


ab\ 


E 


2 (a + b) 

n (l ” 2 ) 


[cos * sin 2ir(ft — ^ 

cos 27 T^ft — ^ J dv . (24) 


This expression may now be integrated over a 
certain region of the wavefront, say from v = v 0 to 
v = v, corresponding to s = s 0 to s = s, giving the 
following expression for the electric field strength 
at P: 


* = k y]w/h) E [ fMsin2ir ( ft -l) 


— g(v,v 0 ) cos 


where 


and 


2 *{ ft - 9 ] 

f(v,Vo ) = J cos (^ I,’ 2 ) dv , 
g(v,v 0 ) = ^ sin (^ i’ 2 ) dv . (27) 


(25) 


(26) 














DIFFRACTION OF RADIO WAVES 


127 


Equation (25) may be brought into a more con¬ 
venient form by writing 


tan 0 


9(v,v o) /oo \ 

fM ’ (28) 

and R = \Zf 2 {v,v 0 ) + g 2 (v,v 0 ) . (29) 

It then follows that equation (26) assumes the form 

E = k 


(30) 


For tabulation purposes the quantities f(v,v 0 ) and 
g(v,vv) are replaced by the Fresnel integrals, defined 


by: 

C v 


cw = J 

o cos (l v *) dv 

(31) 

and 

r v 


sw = J 

o sin (yj dv - 

(32) 

Evidently 

f(v,v 0 ) = C(v) - C(v o)', 

(33) 

and 

g(v,v 0 ) = S(v) — S(v 0 ) • 

(34) 


In the sequel the arguments will be omitted wherever 
it can be done without causing misunderstandings, 
and the above symbols will be written simply as /, 
g, C, and S. 


Table 1 . Fresnel integrals. 


V 

c 

S 

V 

C 

S 

0.00 

0.0000 

0.0000 

2.50 

0.4574 

0.6192 

0.10 

0.0999 

0.0005 

2.60 

0.3889 

0.5500 

0.20 

0.1999 

0.0042 

2.70 

0.3926 

0.4529 

0.30 

0.2994 

0.0141 

2.80 

0.4675 

0.3915 

0.40 

0.3975 

0.0334 

2.90 

0.5624 

0.4102 

0.50 

0.4923 

0.0647 

3.00 

0.6057 

0.4963 

0.60 

0.5811 

0.1105 

3.10 

0.5616 

0.5818 

0.70 

0.6597 

0.1721 

3.20 

0.4663 

0.5933 

0.80 

0.7230 

0.2493 

3.30 

0.4057 

0.5193 

0.90 

0.7648 

0.3398 

3.40 

0.4385 

0.4297 

1.00 

0.7799 

0.4383 

3.50 

0.5326 

0.4153 

1.10 

0.7648 

0.5365 

3.60 

0.5880 

0.4923 

1.20 

0.7154 

0.6234 

3.70 

0.5419 

0.5750 

1.30 

0.6386 

0.6863 

3.80 

0.4481 

0.5656 

1.40 

0.5431 

0.7135 

3.90 

0.4223 

0.4752 

1.50 

0.4453 

0.6975 

4.00 

0.4984 

0.4205 

1.60 

0.3655 

0.6389 

4.10 

0.5737 

0.4758 

1.70 

0.3238 

0.5492 

4.20 

0.5417 

0.5632 

1.80 

0.3337 

0.4509 

4.30 

0.4494 

0.5540 

1.90 

0.3945 

0.3734 

4.40 

0.4383 

0.4623 

2.00 

0.4883 

0.3434 

4.50 

0.5258 

0.4342 

2.10 

0.5814 

0.3743 

4.60 

0.5672 

0.5162 

2.20 

0.6362 

0.4556 

4.70 

0.4914 

0.5669 

2.30 

0.6268 

0.5531 

4.80 

0.4338 

0.4968 

2.40 

0.5550 

0.6197 

4.90 

0.5002 

0.4351 


The Cornu Spiral 

In Figure 20 the two Fresnel integrals are plotted 
against each other, S being the ordinate and C the 
abscissa, for different values of v. The resulting curve 
is known as Cornu’s spiral. The upper positive branch 
(C and S positive) corresponds to points on the 
wavefront above the line. S'P in Figure 19, and the 
lower or negative branch corresponds to the wave- 
front below the line S'P. 

By their definition / and g signify the coordinate 
differences between any two given points on the 
Cornu spiral, and it follows that R, as defined by 
equation (29), represents the corresponding distance 
between these points. 

Differentiating equations (31) and (32) for C and 
S , squaring and adding, it follows that 

(d.cy + (< dS) 2 = (< dv) 2 , (35) 

so that dv is the line element of the spiral, and v 
measures length along the curve from the origin. 

In order to see more in detail how the Cornu 
spiral is built up of contributions from different 
zones we may suppose the half-wave zones on the 
wavefront to be divided into equal areas and the 
contributions of these areas to the field strength 
vectorially combined to obtain the resultant effect 
as in Figure 22. Then as smaller areas are used and 
more zones are summed up the vector diagram 
becomes in the limit the Cornu spiral. This is shown 
in greater detail in Figures 21 and 22. Here the first 
half-period zone of Figure 21 is divided into nine 
parts and the resultant is AB (Figure 22). The 
second half-period gives a resultant BC. The sum 
of the first two half-periods is AC. The sum of all 
half-periods is AZ, which is thus the resultant effect 
at P of the upper half of the wavefront. A similar 
result is obtained for the lower half. 

It may be remarked that the superiority of the 
dimensionless variable v over s shows itself in the 
fact that one Cornu spiral suffices for all situations 
of the diffracting edge, while the use of s would have 
necessitated the construction of a special spiral for 
each specific set of values, a, b, and X. In Figure 20 
the values v = 1 and v = 2 are marked and corres¬ 
pond to path differences A = X/4 and A = X, 
respectively. 

Equation (30) shows that the electric field strength 
in the diffraction region which is due to a certain 
section of the wavefront is proportional to the 
corresponding value of R. Hence, it follows that the 












128 


SITING AND COVERAGE OF GROUND RADARS 



Figure 20. Cornu spiral. 


power per unit area is proportional to R 2 . Let W 
denote peak power per unit area at the point P for 
a certain arbitrary value of R. Then 

W = K • R 2 , (36) 

where K is a certain constant. When the whole wave 
is acting, the integration limits extend from v = 
— co to v = + oo, that is, along the full length of 
the Cornu spiral. The coordinate difference between 
the foci of the spiral being (1,1) (see Figure 20) it 
follows that their distance is R = y/2, so that the 
corresponding peak power per unit area W 0 is, by 
equation (36), Wq = 2 K which defines K as } /£TF 0 . 
Hence it follows that equation (36) may also be 
written as 

W 1 

W-„ = 2 fl2 ' (37) 

1548 Straight Edge Diffraction 

Using Cornu's spiral the diffraction pattern due to 
a straight edge may be obtained. In Figure 23 is 


shown a diffracting edge at M 0 . At P the upper 
half of the wave is effective, and on Figure 22 the 
amplitude is AZ of length l/\/'2. The square of this 
is one-half, which by equation (37) is multiplied by 
K to get Y\ for the power intensity at the edge of 
the shadow. The electric field intensity is }i. 

Consider next a point such as P' at a distance x 
above P (see Figure 23). To be specific, the point 



Figure 21. Division of wavefront into half-period zones. 
















































































DIFFRACTION OF RADIO WAVES 


129 



Figure 22. Vector sum of subzone contributions. 


P' is chosen in the direction of SMi of Figure 23, 
where Mi is the upper edge of the first half-wave- 
length zone. The illumination at the point P' is, 
firstly, due to all wavelets emanating from the half 
wavefront above P'S. In addition, there is the 
contribution from the lower half of the wavefront 
extending from Mi to M Q . The situation is, in fact, 
the same as if P' were brought down to P and the 
diffracting edge were lowered from M 0 to M'{ (see 
Figure 24). The resultant amplitude R is represented 



Figure 23. Diffraction at shadow line. 



on Figure 25 by ZB. Starting at the point P at the 
edge of the shadow (Figure 23) where the amplitude 
is AZ, if the point is moved upward, the tail of the 
amplitude vector moves to the left along the spiral 
while its head is fixed at Z. 

The amplitude goes through a maximum at b', a 
minimum at c', etc., approaching a value ZZ' for 
the unobstructed wave. Moving in the other direc¬ 
tion, into the shadow, the vector moves to the right 
from A, decreasing steadily to zero. 

The power intensity versus v is plotted in Figure 
26, and the points B, C, D, etc., corresponding to 
those in Figure 25 represent the exposure of 1, 2, 3, 
etc., half-period zones below M 0 . The maxima and 
minima occur a little before these points are reached. 
This curve may be plotted from the table of Fresnel 
integrals with the equations 

/ = 0.5 + C , 

g = 0.5 + S , (38) 

* 2 = l(P + g 2 ), 

where z 2 is the relative power intensity compared to 
the unobstructed wave. The relative electric inten¬ 
sity is i f2 , 2 

2 = V 2 • < 39 > 


Equation (39) is plotted in Figure 27. The portion 
of the curve for — v has been drawn to the right and 
is to be used with the right-hand ordinate. 

The phase lag due to diffraction may be deter¬ 
mined from the angular position of the vector R in 
Figure 25. In the illuminated region the phase lag 
oscillates about the reference value, Z'Z, and is 
given by 


tan 


-il 


/■ 


At the shadow line the relative value is the same as 
Z'Z. In the shadow region the phase lag varies 
continuously along a parabolic curve and is given by 
v 2 7 r 

*2 + 5 • 

The phase lag relative to that of the shadow line 
is plotted in Figure 28. The portion of the curve 
for — v is drawn to the right, and its ordinate, on 
the right, has a different scale from that used with 
the -\-v portion of the curve. 


15 4 9 Location of Maxima and Minima 

When the source is close to the diffracting edge, 
the positions of the maxima and minima in the 
















130 


SITING AND COVERAGE OF GROUND RADARS 



Figure 25. Method of using the Cornu spiral. 


illuminated region may be determined by the follow¬ 
ing analysis. The effect of the wave RM (Figure 29) 
at P' may be considered to be due to the upper half 
of the wave (above R), which is unaffected by the 
edge, and the lower half of the wave (below R), 
which is partly shielded by the edge. If RM contains 
an even number of half-period elements the intensity 
at P' is a minimum. If the number of half-period 



Figure 26. Relative power intensity—straight edge 
diffraction. 


elements is odd the intensity is a maximum. That is 

MF' - RP' = ^ , (40) 

£ 

where n is an integer with values 1, 3, 5, etc., for 



Figure 27. Relative electric intensity—straight edge 
diffraction. 


z RELATIVE INTENSITY 
































DIFFRACTION OF RADIO WAVES 


131 



Figure 28. Phase lag—straight edge diffraction. 


maxima and 2, 4, 6, etc., for minima. The difference 
MP' — RP' is a constant, and the locus of the 
point P' is a hyperbola having M and S for loci. 
That is, 

SP' - MP' = SR - (. MP' - RP'), (41) 


Therefore from equations (40) and (41): 

MP’ - RP' - (1 - -J_ )„ >| ; (42) 

hence 

- = ^ , (43) 

where n is odd for maxima and even for minima. 



and SR is constant; therefore, the difference of the 
distances of P' from the fixed points S and M is 
constant. P' describes a hyperbola, but its curva¬ 
ture is so small that it almost coincides with its 
asymptotes. 

The distance x to a maximum or minimum may 
be computed as follows 

Since x is small compared to a + b 


SP 1 


a + b + 


2 (a + b) 


also 


MP' = b + 


2 b 



Figure 29. Path differences at a straight edge. 


15.4.10 The Rectangular Slit 

A problem similar to the straight edge is the 
rectangular slit (see Figure 30). Cornu’s spiral will 
be used to determine the field intensity along the 
plane PP'. With the slit in the central position, the 
only radiation at the plane is due to the wavefront 
in the interval As = MN. Equation (31) is used to 
determine what length Ay corresponds to As. The 
resultant field strength at P is given by the chord 
of the spiral which has a length Av. Since the point 
of observation P is centrally located, this chord will 
be centered on the spiral. Thus, if Ay = 0.5 the 
chord (see Figure 20) will extend from approximately 
C = -0.25 to C = +0.25. The resultant R ^ 0.5 
substituted in equation (37) gives a power intensity 
of % relative to the unobstructed wave and a field 
strength of 0.353. 

The field intensity at P' is due to the same length 
Ay but taken over a different portion of the spiral. 
For this purpose, it is desired to use distances along 
the plane PP', x, instead of s (Figure 30). 

<«> 

Thus the portion of the spiral nO in Figure 31 from 
y = 0.9 to y = 1.4 has an average value of v = 1.15 
which multiplied by the radical term of equation (44) 
gives x. The chord connecting these points is 0.43, 
































132 


SITING AND COVERAGE OF GROUND RADARS 



and the relative power intensity is 0.092. This same 
result may be computed from the table of Fresnel 
integrals by obtaining the values of A C and AS for 
v = 0.9 and v = 1.4. The sum of the squares of A C 
and A*S is R 2 . Typical patterns for slits of several 
widths are shown in Figure 32. It will be noted that 
there is little radiation outside the slit. 

i54.il J)iff rac tion by a Narrow Obstacle 

The effect of a narrow object with parallel sides 
may be determined with the Cornu spiral. In the 
case of the slit only a fixed length slid along the 
spiral is effective, the remainder being shielded by 
the edges of the slit. With an obstacle, however, a 
fixed length slid along the spiral represents the 
ineffective portion. If the obstacle is of such size 
that it covers an interval Av = 0.5 on the spiral, 
Figure 31, the segment Av may be located as JK. 
The radiation at the point considered will be due 


Av s 1.5 

■JL 


-5 0 +5 


-3 0 +3 


Av= 2.5 


2L 


0 +4 


Av = 5.2 




-3 


0 +3 


A v -3.9 A v =6.2 



-6 -3 0 +3 +6 


Figure 32. Diffraction patterns of slits. 
















DIFFRACTION OF RADIO WAVES 


133 


to the two parts of the spiral Z' to J and K to Z. 
The resultant amplitude is obtained by adding the 
two vectors Z'J and KZ. The sum is R for a point 
midway between J and K. The head of the vector 
is always in the direction Z along the spiral. Typical 
patterns for narrow obstacles are shown in Figure 33. 


made of the effect of the shape and composition of 
the edge. Actually within a region of about one 
wavelength around the edge the wavefront is 
affected by the presence of the edge. In Figure 34 
the region of the edge disturbance is DE, and first 
half period of the wave front is DF. The first half 




Multiple Slits and Obstacles 

Slits or obstacles with parallel sides may be treated 
by means of the Cornu spiral and the resultant sum 
of the vectors obtained. Thus, with two slits of a 
width such that Ay = 0.5 and spaced so that Ay = 0.5 
may be located on the spiral as JK and Im in 
Figure 31. The total R is the vector sum of R and 
R". The field strength pattern is then obtained by 
sliding the two lengths along the spiral holding their 
spacing fixed. 

In similar fashion two narrow obstacles would 
cause two absent sections such as JK and Im and 
three open sections Z'J, Kl, and mZ. The three 
vectors, obtained by joining these three latter pairs 
of points, are combined to give the resultant ampli¬ 
tude R. 

15.4.13 Limitations of Fresnel’s Theory 

Neither Huyghens’ principle nor Fresnel’s theory, 
on which the above treatment is based, is rigorous, 
and their limitations must be kept in mind when 
making applications to radio and radar problems. 

In the development of the theory no mention was 



Q_Pj 

Figure 34. Edge effects. 

turn of the Cornu spiral is due to DF. The position 
of F depends on the point considered. When DE is 
an appreciable part of DF, the simple Fresnel theory 
should not be depended upon. This occurs when the 
field point is at Q, lying at a large angle of diffraction, 
or at R, close to the edge. 

Near the diffracting edge, a certain amount of re¬ 
flection occurs, especially near R. This reflection is 
divergent and decreases rapidly in intensity as one 
recedes from the edge. When the edge is blunt or 
has a large radius of curvature, the amount reflected 
is increased and the field is affected over a greater 
distance. Since the angle is near grazing, the nature 
of the reflecting surface is not important. If Fresnel’s 
theory is applied to spheres and cylinders, the results 
may be only approximate. 

When the edge and the electric vector are parallel, 
the theory gives good results. When the electric vec¬ 
tor is perpendicular to the edge, the field strength in 
the shadow region may be several times larger than 
that obtained with the electric vector parallel, and 
the theory should then be used only for small angles 
of diffraction. 

Other discrepancies are due to ignoring the ob¬ 
liquity factor and the effect of the inclination of the 
wavelets with respect to each other. The theory does 
not give the correct phase angle for the diffracted 
wave. 

The same objections may be raised for apertures 
and obstacles whose dimensions are of the order of 
a wavelength. 















134 


SITING AND COVERAGE OF GROUND RADARS 


It should be noted that 

1. Fresnel’s theory is valid when the wavelength is 
small compared to the dimensions of the diffracting 
object (as in optics). 

2. Fresnel’s theory should not he used: 

a. For large angles of diffraction. 

b. Close to the diffracting edge. 

c. For apertures or obstacles of the order of a 
wavelength. 

d. When the diffracting edge is not parallel to 
the direction of polarization of the wave. 

In spite of these shortcomings the theory is useful 
because it provides simple solutions for the majority 
of the diffraction problems encountered in the field, 
and, considering the difficult nature of the general 
problem, it is still the most manageable treatment 
that has been developed. 

155 PERMANENT ECHOES 

15,51 Introduction 

Permanent echoes are due to reflection from terrain 
features such as mountains, islands, oj* even smooth 
surfaces near the antenna (ground clutter). Nearby 
hills and surfaces produce strong echoes which 
obscure the indicator and widen the main pulse so 
that the minimum range of detection is increased. 
More important are the distant hills, especially those 
in the operating sector which obscure areas of tactical 
importance. Permanent echoes are a prime considera¬ 
tion in siting, as many otherwise excellent sites are 
rendered worthless by excessive fixed echoes. A care¬ 
ful analysis of the terrain will enable an approximate 
prediction of such echoes. In this section is presented 
a systematic method of preparing permanent echo 
predictions so that the suitability of sites may be 
determined without actual field tests. 

Several factors combine to make permanent echoes 
more troublesome than might be expected on first 
thought. 

1. Hills and land surfaces are so much greater in 
extent than the target which the equipment is 
designed to detect, that strong echoes may be 
obtained from distances where an ordinary target 
would give an echo far below normal detection levels. 

2. The low elevation of the land surfaces places 
them in regions most subject to nonstandard propa¬ 
gation effects where extreme ranges and large 
responses are frequently obtained. 

3. Side lobes of the horizontal pattern of the 


antenna cause permanent echoes to appear at several 
other azimuths in addition to that of the main lobe. 
Although the signal intensity of the side lobes is 
much reduced, the echoes may still be strong enough 
to obscure targets. 

4. Strong permanent echoes causing considerable 
trouble may be obtained from distant mountains in 
the rear as a result of back radiation. Again, the 
weakness of the radiation and distance of the moun¬ 
tains are often compensated for by the large extent 
of the reflecting surface. 

5. Antennas with wide beams cause permanent 
echoes to be much wider than the object that 
produces them. 

6. Diffraction over intervening ridges is often 
sufficient to nullify their screening action so that 
objects behind the ridge are visible. 

Permanent Echo Diagrams 

The permanent echoes associated with a radar 
station may be plotted on a chart and their extent, 
location, and strength represented. Permanent echo 
diagrams should be prepared for each unit of a radar 
system using a standard procedure for the taking 
and presentation of data. These diagrams are very 
useful for: 

1. Indicating blind areas in a station’s coverage. 

2. Assigning the operating area of a station. 

3. Checking the range and azimuth accuracy. 

4. Checking the transmitter output and receiver 
sensitivity. 

5. Estimating nonstandard propagation. 

6. Planning test flights. 

While methods used in different theaters vary as 
to detail, the typical permanent echo diagram is 
prepared about as follows. The equipment should 
be in normal operating condition: that is, the trans¬ 
mitter output and receiver sensitivity should be as 
recommended by the instruction manual; the range 
and azimuth calibrations should be accurate; and 
the weather conditions that affect propagation should 
be average. The receiver gain should be set to some 
standard level, usually maximum, or to some definite 
noise height. The value of the data taken will depend 
to a considerable extent on the skill and judgment 
of the operator. The station would normally be taken 
out of operation for about an hour while data are 
taken, although it is possible to take observations 
during normal scanning by stopping momentarily. 
Where antenna switching is provided, the low-angle, 



PERMANENT ECHOES 


135 


long-distance beam should receive the most atten¬ 
tion although the other combinations should be 
checked also. 

If the beam is highly directive and can be changed 
in elevation, a low angle such as would be used for 
distant search should be used for recording perma¬ 
nent echoes. In some situations several elevations 
should be used. On plan position indicator [PPI] 
scopes it may be more convenient to photograph the 
screen if proper equipment is available. Care should 
be taken not to confuse storm and fog echoes with 
permanent echoes on microwave sets. 

A more detailed procedure is required where A- 
scope presentation is used. After the initial adjust¬ 
ments have been made the next step is to decide on 
the intervals in azimuth at which readings are to 
be made. The definition of the echoes will depend 
in part upon the beam width so that the narrow 
beam radars should be checked at closer azimuth 
intervals. Readings may be taken at intervals of 10° 
or 5° or even less depending upon the detail desired; 
in general an interval of about a fourth of the beam 
angle is sufficient. Permanent echo readings should 
be taken through 360° regardless of the sweep sector 
used, so that back and side echoes may be investi¬ 
gated also. 

At each azimuth the range of all permanent echoes 
is recorded from zero out to the extreme range. The 
width of the main pulse and local ground echoes 
should be noted as well. Echoes one mile or less in 
width are recorded by a single reading at the center 
of the echo. Wider echoes are recorded by two read¬ 
ings, one at the left of the echo where the trace leaves 
the baseline and a second at the right where the 
trace returns. Adjacent echoes less than 1 mile apart 
are recorded as a single echo. Where the separation 
is greater, care should be taken not to lump echoes 
together. 

For most purposes variations in amplitude may 
be disregarded. Amplitude is, however, sometimes 
recorded for a few azimuths of special interest such 
as those used for test flights or in tactically important 
regions. 

To plot the data an overlay of a regional aero¬ 
nautical map or other chart with a scale of 1 to 
1,000,000 may be made showing some of the signif¬ 
icant features as coastlines, islands, and cities. On 
this should be drawn radial azimuth lines every 10 
degrees and range circles every 10 miles. The data 
are then marked on the chart as short lines, and 
these lines are connected as indicated by inspection. 


The enclosed areas may then be shaded lightly. If 
it is desired to represent amplitudes, a few equal 
amplitude contours may be shown within an echo 
area. More detail may be shown by plotting ampli¬ 
tude versus range on a rectangular graph for each 
azimuth. 

The completed permanent echo diagram should 
be compared with a topographical map to check the 
degree of shielding obtained and the range and 
azimuth accuracy of the equipment and back and 
side lobe radiation effects. Care must be exercised 
in identifying the cause of an echo, as distant echoes 
may come in on the second or third sweep on the 
scope after the main pulse. 

In Figure 35 is shown a permanent echo diagram 
which was selected for purposes of illustration rather 
than as an example of a good site. A few miles from 
the coast is an extensive range of mountains which 
are poorly shielded to the north. The large echo at 
200° is due to a mountainous island 260 miles away. 

15 5 3 Use of Permanent Echoes in Testing 

Permanent echoes are useful for tuning the equip¬ 
ment, estimating the output and sensitivity, and 
checking the range and azimuth accuracy. While 
such observations may be used as an overall test 
of performance, care should be used in selecting the 
test echo and in interpreting the indications. 

Careful tests have shown that, even though 
equipment performance is closely controlled, the 
strength of permanent echoes varies over a consider¬ 
able range. It is noted further that indications from 
aircraft also vary, but there is little correlation with 
the changes in permanent echoes. Other tests show 
that, as the performance of the set is reduced, the 
maximum range for small targets is reduced at a 
much faster rate than for large targets. Thus a 
reduction of receiver sensitivity may cause weak 
echoes to disappear entirely without a noticeable 
effect on strong permanent echoes. 

Permanent echoes vary for the following reasons: 

1. Atmospheric changes affect both the direct and 
reflected rays. This may be due to a change in the 
amount of refraction from standard or in the degree 
of trapping. Under some conditions marked absorp¬ 
tion may occur. The changes may occur slowly or 
fluctuate erratically, being most marked in connec¬ 
tion with microwaves. 

2. If the reflecting surface is the ocean, variation 
of the reflected ray may occur if the tide changes 




136 


SITING AND COVERAGE OF GROUND RADARS 



or the roughness of the surface becomes excessive. 

3. Frequency variations will affect the echo from 
complex reflectors such as rugged terrain. Peaks 
which are separated in distance such that the returns 
from a single pulse overlap are said to be frequency 
sensitive. In the overlap portion the echo strength 
will depend upon the relative phase of the two 
returns. Thus if the pulse width is 10 jusec the wave 
train will be about 2 miles long. If there are peaks 
at 10 miles and 10M miles their echoes will appear 
as follows on an A scope: 

10 to 10}4 miles near peak echo only 


10J/£ to 12 miles combined echo of both peaks 
12 to 1234 miles far peak echo only 

The combined portion of the echo may have a height 
from zero to twice that of the individual echoes and 
usually fluctuates rapidly as the frequency drifts. A 
change of a half wavelength in the separation of the 
peaks will change the combined echo from maximum 
to minimum. This means that a frequency stability 
of the order of one part in a million is required for 
a steady combined echo. 

Permanent echoes used for testing should therefore 
be (1) nearby but distinct from ground clutter and 

















































PERMANENT ECHOES 


137 


other echoes, (2) separated from the transmitter by 
rough nonreflecting land, (3) a single distinct target 
such as a steel tower, (4) weak in response, that is, 
comparable to that of a distant aircraft. 

The range of echoes which come in on the second 
or third pulse may be estimated by adding one or 
two times the length of the range scale to the 
observed range plus an allowance for the return 
trace time, usually several miles. To determine by 
test which sweep an echo is associated with, the 
pulse repetition rate should be changed, and the 
shift in range of the echo observed. Thus if the range 
scale is 200 miles long and the pulse rate is reduced 
10 per cent, then a target at 250 miles which had 
been appearing at 48 miles would shift to an indi¬ 
cated range of 23 miles and could thus be distin¬ 
guished from a 48-mile target that would shift to 
43.2 miles. 

Frequency-sensitive permanent echoes are not 
suitable for checking range accuracy. The frequency 
changes from maximum to minimum return are 
usually too small to be detected on a frequency 
meter, so that frequency-sensitive echoes are recog¬ 
nized chiefly by their unsteady appearance. 

Azimuths may be determined to best accuracy 
by “beam splitting.” This consists in turning the 
antenna slightly to one side of the maximum until 
the signal decreases to a predetermined level. The 
antenna is then turned past the maximum until the 
same level is reached and the two azimuths are 
averaged. When checking azimuth accuracy the 
possibility of horizontal diffraction due to a nearby 
hill should be considered. 

1554 Shielding 

The principal device for control of fixed echoes is 
shielding. This means that the antenna is to be sited 
in such a way that distant hills are screened by a 
local obstruction. A local echo at say 3 miles, is 
combined with the main pulse or ground return, 
and the distant echo is weakened or eliminated 
entirely. In operating regions the loss of coverage 
may be more serious than the permanent echo, so 
shielding should be used with caution. 

Rear areas which are not scanned should be well 
shielded so that back and side echoes do not interfere 
with targets in important tactical regions. Operation 
over such shielded sectors would be limited to high 
targets. 

Construction of artificial shields made of poultry 


netting has been suggested in some cases, where the 
back radiation and side lobes were relatively strong. 
The very large size of such structures ordinarily 
renders them impractical. Most of the antennas 
using parabolas have a small back radiation, and 
permanent echo problems are much simpler. 

In special cases it may be desirable to eliminate 
a particular echo from some obstacle without using 
shielding. This may be done by constructing a target 
of sheet metal on the side of the obstacle, spaced so 
that the target echo and obstacle echo are about 
180° out of phase. This requires accurate alignment 
of the target (so that it is normal to the radiation to 
within 5° or less) and close control of the frequency. 
It is also necessary that the area be adjusted so that 
the response of the target and obstacle are equal. 

15.5.5 Prediction of Permanent Echoes 

Permanent echoes may be determined by several 
methods: 

1. Tests with the radar at the site. 

2. Profile method. 

3. Radar planning device [RPD]. 

4. Supersonic method. 

The feasibility of moving the radar to the site to 
determine the permanent echoes is dependent on 
portability, accessibility, etc. Echoes obtained with 
one type of equipment may be very different from 
those from another type of radar with different 
directivity, frequency, and range. 

The profile method, which will be described in 
detail below, involves a study of topographical maps 
and plotting the echoes according to their visibility 
and the amount of diffraction. A fairly difficult site 
may be handled in perhaps 8 man-hours. This method 
is adapted to long-range, low-frequency radars where 
diffraction and side and back lobe radiation are 
important. On microwave equipment fixed echo 
prediction is simpler and the profile method may be 
worked out in a few hours. 

The RPD technique requires construction of a 
relief model of the terrain considered. A small light 
source is used to simulate the radar and the echoes 
are plotted as a result of a study of the areas illu¬ 
minated. This method is adapted for short ranges 
and microwaves where the diffraction and side and 
back lobe radiation are small. Construction of a 
fairly difficult model may take a crew of men several 
days to a week, as a model should be accurate. 



138 


SITING AND COVERAGE OF GROUND RADARS 


Once completed, all possible sites or aspects from a 
plane or ship may be readily examined. Models of 
enemy areas may be used to predict the coverage 
of possible enemy sites, and evasive action may be 
planned. The RPD is well suited for training and 
briefing of air personnel. Kits are provided contain¬ 
ing the light source, supports, etc. Darkroom facilities 
are required, and special processing of films is used 
to secure more realistic pictures. 

The supersonic method requires a model made of 
sand, glass beads, etc., to be used under water. Such 
models are much easier to construct than the RPD 
type. Supersonic gear is used to send out pulses 
which are reflected like radar pulses and the echo 
is picked up and presented on a PPI scope. Photos 
may be taken of the scope picture, and the method 
may also be used for training and briefing. Special 
equipment is required, but the models may be made 
easily and the presentation is obtained direct on the 
PPI scope without further processing. This method 
is well adapted for training, as flight, changes in 
altitude, etc., may be simulated readily by movement 
of the sonar head. 

In general the profile method should be used on 
long waves or on microwaves where only a few sites 
are being considered. It is well adapted for the 
estimation of nonstandard atmospheric effects. For 
air- or ship-borne radar the RPD or supersonic 
methods are convenient because of the large number 
of aspects involved. It may be noted that the latter 
two methods should not be considered more exact 
than the profile method, as the principle of similitude 
does not apply unless all elements including the 
wavelength are changed in proportion. The principal 
difficulty is to secure a source which has the same 
radiation characteristics as the antenna system. 

Prediction by Profile Method 

The profile method will be described in detail. The 
discussion will refer chiefly to YHF radars in a 
mountainous terrain, but the methods have general 
application. The principal requirements are topo¬ 
graphic maps of the surrounding area with a scale 
of 1 or 2 miles to the inch and a contour interval 
of 20 ft, although intervals up to 100 ft may be 
used. Maps with a scale of about 20 miles to the 
inch are needed for checking distant echoes. Regional 
aeronautical maps, with a scale of about 1 inch to 
16 miles and 1,000-ft contours, are suitable as the 
height of prominent peaks is indicated. 


From the maps, profiles are prepared for various 
azimuths about the radar station. The first mile or 
so should be plotted accurately, and at greater 
distances the critical points such as hills and breaks 
should receive the most attention. A convenient 
scale is 2 miles to the inch for range and 500 ft to 
the inch for elevation. The distances to which the 
profile should be plotted is a matter of judgment, 
but it should be extended to perhaps 20 miles, or 
further if there is doubt. 

On each profile is drawn the tangent line from the 
center of the antenna to the point on the profile 
which determines the shielding, as in Figure 36. 



Figure 36. Typical profile. (Note: T in degrees). 

This is the line-of-sight curve; it is drawn for each 
azimuth, and the vertical angle y is marked on the 
profile. If the angle is below the horizontal it is 
negative, and caution must be used on high sites 
not to exceed the limiting shielding angle of the 
radar horizon. This is given by the expression 

7 = -0.0108 a/2/Ti , (45) 

where y is the angle between the effective horizon 
and the horizontal at the antenna in degrees and hi 
is the height of the center of the antenna in feet. 

The line of sight is actually curved, as explained 
in the section on visibility problems, but for ranges 
up to 10 miles the error in using a straight line is 
small. For longer distances the dip QX as computed 
from equation (5) should be considered. More con¬ 
venient for this purpose are the curves of the line 
of sight for various angles which are calculated from 
Figure 37. Standard refraction is taken into account 
by use of % a instead of a for the earth’s radius, 

| a = 1.33 X 3,960 = 5,280 , 

d 2 (46) 

h 2 — hi = 5,280 d tan y + —, 

with hi and h 2 in feet and d in miles. Above 10°, or 
where the shielding is distant, equation (8) should 
be used. 













PERMANENT ECHOES 


139 



Figure 37. Line-of-sight geometry. 


These curves are plotted in Figures 38 and 39, and 
their use is illustrated in Figure 36. The center of 
the antenna is at 200-ft elevation, and the height 
of the shielding ridge 4 miles away is 400 ft. For a 




Figure 39. Line-of-sight curves. 


200-ft rise in 4 miles the angle is found from Figure 
38 to be 0.5 degree. This curve can then be used to 
determine the height of the shielded region at other 
ranges. Thus the range at which the shielded region 
is 4,000 ft high for the case considered is found from 
Figure 39 by using /* 2 — hi = 4,000 — 200 = 3,800 
ft for height and the ^-degree curve, giving 53 miles. 

It is desirable to be able to estimate diffraction 
effects in a simple fashion suited to the approximate 
nature of this kind of work. As shown in Section 
15.4.8 the field intensity varies in a rather compli¬ 
cated manner with the diffracting angle 6 d and the 
distance of the shield cfi [Figure 7 and equation (10) ]. 
In Figure 40 is plotted the relative field intensity 
compared to that obtained without a shield for 
shields at several distances. This graph is intended 
for S00 me but may be used on other frequencies by 
changing di in proportion to the change in X. It 
enables one to make an estimate of the effectiveness 
of a shield. Thus if a shield is 1 mile away it may be 
neglected for values of 6 d in excess of +3°. Likewise 


Figure 38. Line-of-sight curves. 













































140 


SITING AND COVERAGE OF GROUND RADARS 



Figure 40. Diffraction over a ridge. (200 me) (For other frequencies change d\ in proportion to the change in wavelength.) 


objects below —3° in the shadow region would give 
weak echoes in most cases. For intermediate angles 
the relative intensity may be read from the curve. 
For shields closer than 0.1 mile the methods of 
Section 15.4.8 should be employed. 

Figure 15 shows that the relative intensity of a 
diffracted wave is virtually constant for a given 
angle when the distance from the edge is large. 
Equation (22) may then be written in the form 



where 6 d is in radians (1 radian = 57.3°) measured 
from the geometrical shadow line (Figure 7) and 
d\ is in the same units as X. This equation is approxi¬ 
mate, and the error is of the order of a/b. 

Where the shield consists of several ridges close 
together, an equivalent shield is used instead of 
successive shields. The height and distance of the 
equivalent shield is found by constructing a triangle 
between the radar and the reflecting object which 
encloses the shielding ridges. The apex of this triangle 
is then treated as though it were the diffracting 
edge. In Figure 41 H and d\ are the quantities to 
be used in equations (10) and (47). 

The general procedure to be followed in preparing 



a prediction of permanent echoes will now be out¬ 
lined. By examining a topographical sheet the azi¬ 
muths are determined at which profiles should be 
prepared. This will normally be about every 10 
degrees. Where the shielding is obviously good the 
interval may be 20 degrees, but where the terrain 
is questionable such as a region of low hills the 
profiles should be taken at 5-degree intervals. The 
profiles are prepared and the angle of the line of 
sight determined as described above. 

The next step is to make an overlay of a map of 
scale 1 to 1,000,000. The principal features as coast¬ 
line, towns, and rivers are sketched in to aid in 
reading the completed chart. On this is drawn a 
polar coordinate system with azimuths marked every 
10 degrees and range circles every 10 miles out to 
the full range of the indicator. 

On the overlay are now drawn the coverage 
contour lines. These lines represent the limits of 
the heights of the shielded regions. Targets or 
mountains below these coverage contours will not 




























PERMANENT ECHOES 


141 


be visible except by diffraction, and targets above 
the contours are in line of sight and receive direct 
radiation. For each azimuth and the corresponding 
angle of sight (Figure 36) the ranges are plotted for 
various contour heights as 1,000, 5,000, 10,000, and 
15,000 feet. Where these coverage contour lines are 
close together the shielding is good but the coverage 
is poor; where the lines are widely separated, the 
shielding is weak, and toward the sea there is no 
shielding except by the horizon. 

With the coverage contour diagram superimposed 
on a map, the peaks exposed to radiation may be 
noted. The extent of the echoes due to these peaks 
depends on the horizontal radiation pattern and 
pulse width. The horizontal beam width is only a 
very rough measure of the width of an echo, and 
some other angle usually between the half-power 
points and the nulls will determine the echo width. 
The angle may be estimated by considering the range 
and size of the peak. The extension of the echo in 
range will be at least as great as the pulse width in 
miles, which as it appears on the indicator is about 
0.1 mile per nsec. Actual echoes are usually much 
wider than this, as all of the exposed hill sends back 
an echo. 

The echoes are then sketched in, based on inspec¬ 
tion of the profiles. The plotter’s judgment is a very 
important factor, but the following rules may be 
used as a guide. 

1. Shade in a circle for the main pulse several 
miles wide, depending on the pulse width and local 
return. 

2. Consider each profile in turn and for each peak 
or hillside in front of the shielding plot an echo on 
the main and all sidelobes. 

3. A series of sharp hills within the shielding 
region should be plotted as a single echo rather than 
a number of echoes. 

4. The inner edge of an echo should be at the same 
range as the hill, and its extension depends on the 
slope of the hill and the pulse width, which may be 
several miles with some sets. 

5. In case of doubt plot the echo. 

6. Peaks beyond the shield may be in the diffrac¬ 
tion region and the relative intensity of the radiation 
at these peaks will then be obtained from Figure 40 
as described above. 

7. If the mountain is large enough to intercept 
several lobes, the interference effects may be ignored. 
The echo strength may be estimated roughly as 
proportional to the cross-sectional area of the moun¬ 


tain, the relative intensity of the radiation from 
Figure 40, and the inverse square of the distance. 
For side and back lobes an additional factor is 
required. 

8. The 1 to 1,000,000 scale map should be carefully 
checked to make sure that no peaks are missed in 
between the azimuth considered or at extreme ranges. 

In the above method much is left to the judgment 
of the plotter but it will be found that with experience 
a reasonably good estimate of permanent echoes may 
be made from a map. 

Example 8. Profile Method. A detailed example of 
a difficult site will be worked out, and comparison 
will be made with the actual recorded echoes. The 
site selected is that of Figure 35. The characteristics 
of the SCR-270B radar are given in Table 2. 


Table 2. Type SCR-270B. Characteristics of antenna 
pattern. 



Horizontal pol. 

Vertical pol. 

Half-power beam angle 

26° 

6.5° 

First null angle 

40° 

14° 

Secondary lobe angle 

45° 


Secondary null angle 

90° 


Secondary lobe angle 

5% 


Back radiation 

4% 



Other characteristics of this set are as follows: 

Pulse width 30 nsec = 3 miles 

Nominal range 150 miles 

Sweep sector 185° to 290° 

Elevation: center of antenna 387 ft 

From these data may be calculated the relative 
echo strengths of mountains at various distances 
and the relative side and back echoes. A reference 
value of 1.0 is taken for the main echo from a typical 
mountain 100 miles distant, and the relative intensity 
from Figure 40 is taken equal to 1.0. It is estimated 
that all echoes whose strength compared to the 
reference value is over 0.25 will be strong enough to 
obscure targets. Thus the back echo of a mountain 
10 miles away in a diffraction region where the 
relative strength is 0.5 would have an echo value 
of (100/10) 2 X 0.5 X 0.04 = 2.0 and should be 
plotted since it exceeds 0.25. 

A table may be constructed for the main, side, 
and back lobes ( M , S , B) for various distances and 
degrees of diffraction to show which echoes should 
be plotted. Table 3 is such a table, corresponding to 
a reference strength equal to 0.25. This table will 
apply only for the conditions of this example. 









142 


SITING AND COVERAGE OF GROUND RADARS 



Table 3. Prediction of permanent echoes.* 
Relative intensities from Figure 40. 

Distance 


in miles 

1.18 

1.00 

0.75 

0.50 

0.25 

0.10 

0.03 

1 

MSB 

MSB 

MSB 

MSB 

MSB 

MSB 

MSB 

10 

MSB 

MSB 

MSB 

MSB 

MSB 

MSB 

M 

20 

MSB 

MSB 

MSB 

MSB 

MSB 

M 

M 

50 

M 

M 

M 

M 

M 

M 


100 

M 

M 

M 

M 

M 



200 

M 

M 







*This table will apply only for the conditions of Example 8. 


In Figure 42 is shown a topographical map of the 
area. Contours are drawn for the first few thousand 
feet, and prominent peaks are indicated. From topo¬ 
graphical sheets of a 20-ft interval and a scale of 
2 in. to the mile the profiles of Figures 43 and 44 
are obtained. From the center of the antenna to the 
“effective” shielding, the line of sight has been drawn 
and the angle of the line of sight noted. In some cases, 
as at 20 degrees (Figure 43) a near sharp ridge is not 


















































PERMANENT ECHOES 


143 







1* 







O DEGREES 























Figure 43. Profiles for Example 8. 


7* 


1 


v 





SO 

DE 

SRE 

:es 










A 

uj 
















500 

o 



< 



3.5* 

1 




IOO 

DEGREES 








s 




1l 


, r 

















V/ 

y 

V 













500 






1-1- 




I20' DEi 

GRE 

:es 






























f 




500 


■DEGREES 


160 DEGREES 


0 1 2 3 4 5 6 

RANGE IN MILES 


Figure 44. Profiles for Example 8. 


the north the numerous mountains are unshielded 
and give rise to many echoes which extend into the 
search sector to the west. The islands are inherently 
bad and cannot be shielded without drastic loss of 
coverage. In some cases, as along azimuth 345°, 
ridges which cause large echoes shield more distant 
ridges. The broken terrain in this region is taken to 
give one large echo rather than a number of small 
echoes. In most cases the simple rules for plotting 
echoes may be applied directly. 

Where diffraction is involved the procedure should 
be more detailed. In Figure 43 azimuth 20° will be 
examined to determine the visibility of the hill at 
4.65 miles. The following data are obtained from 
the profile. 

hi = 387 ft; d\ — d\ = 1.45 miles 

h 2 = 550 ft; d' 2 = 3.20 miles 

H = 425 ft; d\ = 4.65 miles 

From equation (8): 

, _ 4.65 X 550 - 3.20 X 387 4.65 X 3.20 

4.65 - 3.20 + 2 

= 917.2 ft . 


From equation (10): 


Ba = 


425 - 917.2 
5,280 X 4.65 


X 57.3 = 


-1.15° . 


From Figure 40 the intensity is found to be 15 
per cent. At the very short range of this hill a strong 
echo would be expected at this intensity, and all 
lobes would be plotted. 

At 138.5° azimuth and 160 miles is a 10,000-ft 
mountain (not shown in any figure). The data for 
this case are: 


considered an effective shield because of the large 
diffraction around such obstacles. The map is 
inspected between the azimuths used and the hori¬ 
zontal limit of shielding of a ridge noted. Thus the 
shielding ridge on 120 degrees (Figure 44) is found 
to drop off at 138 degrees. From the curves of 
Figures 38 and 39 are read the ranges for h 2 — hi = 
1,000, 5,000, 10,000, and 15,000 ft for the line-of- 
sight angles at various azimuths. These points are 
plotted on Figure 42; they are connected by heavy 
dashed lines and are the coverage contours. 

In Figure 45 are plotted the predicted echoes. It 
will be noted that the shielding to the east is very 
good and most of the mountains are not visible. To 


hi = 387 ft; d\ — d\ = 0.27 miles 

h 2 = 380 ft; d'i = 160 miles approximately 

H = 10,000 ft; d 'i = 160 miles approximately 

160 X 380 - 160 X 387 160 X 160 

0.27 + 2 

= 16,950 ft. 


Bd 


10,000 - 16,950 
5,280 X 160 X 


-0.472° . 


From Figure 40 the relative intensity is 43 per 
cent. A main lobe echo is plotted on the second sweep 
at 10 miles since the first sweep is only 150 miles. 

In Figure 35 is shown a large echo at 110 miles 
from 175 to 242 degrees. This is received only when 






























































































































































































144 


SITING AND COVERAGE OF GROUND RADARS 



Figure 45. Predicted permanent echoes. (Example 8.) 


there is trapping, and the size of this echo indicates 
the unusual weather conditions at the time the data 
were taken. This echo is due to a mountainous island 
260 miles away and about 5,000 ft high. There is 
no shielding except from the curvature of the earth. 
The relative intensity compared to the free space 
intensity computed from the formulas for the dif¬ 
fractive region (not given here) is 0.5 per cent. This 
echo would not ordinarily be plotted in spite of the 
large area of the mountain side. 

In correlating the predicted and actual fixed echo 
diagrams, Figures 45 and 35 respectively, it will be 


noted that the degree of success achieved depends 
on the effort expended. Numerous small echoes were 
not predicted, but these are unimportant from an 
operating standpoint. “Permanent” echoes vary over 
wide limits with changes in weather conditions and 
efficiency of the equipment so that only a fair 
agreement should be expected in their predictions. 

Microwave Permanent Echoes 

With microwave equipment a simple analysis of 
the terrain is generally sufficient. The beam may 







































THE CALCULATION OF VERTICAL COVERAGE 


145 


be treated virtually as a searchlight, as the back 
radiation and diffraction effects are small. Trapping 
is likely to be severe and in some regions it is the 
controlling factor. Sea or land clutters are important 
and the extent of such echoes may be estimated 
from equation (16). 

Microwave sets because of their narrow beam- 
width, high resolution, and PPI presentation are 
well adapted to navigational uses. Coastlines may 
be readily identified, and ships near land may 
accurately determine their position. Over land it is 
frequently difficult to correlate a PPI picture with 
a map. In many cases it may be very desirable to 
be able to locate terrain features accurately. 

The presence of some distinctive echo is of great 
assistance in orientation of the picture, but scope 
distortions and the nature of the echoes cause much 
confusion. It is therefore desirable to be able to 
correct the distortions and to be able to prepare a 
radar map which shows the terrain features likely 
to contribute to the observed pattern. 

The PPI distortions are due to the beamwidth, 
range marker errors, and nonlinear sweep. The 
width of the beam causes objects to appear wider 
than they are, as discussed in preceding sections. 
The range marker errors may be determined by 
calibration with a precision-type calibrator. By 
preparing a cardboard scale to line up with the range 
pips the correct ranges of echoes may be obtained. 
Because the sweep usually takes about 15 gsec to 
attain a steady speed the pattern is displaced inward 
with respect to the map. This may be compensated 
in part by adjusting the centering control so that 
at least one of the range markers is moved out 
radially to its true range. The pattern will then 
show a central hole, and the first half mile will be 
displaced from its true position, but the pattern 
as a whole will be more accurate. 

For construction of the radar map it is desirable 
to have topographic sheets of a scale of 1 to 20,000 
which show modern structures. Aerial photographs 
are also useful. Map matching is done by adjusting 
the sweep length and centering controls with major 
changes in scale made photographically. To eliminate 
detail of little interest it is desirable to ink in only 
those contours which correspond to equal increments 
of radar range based on the curved surface of the 
earth. That is, the retraced contour intervals should 
form a sequence of squared numbers (1, 4, 9, 16, 
25 • • • n 2 ), for example, 20, 80, 180, 320, and 500 ft. 
The amount of distortion to introduce into the radar 


map is obtained from the range correction scale and 
the shift of the PPI center. For each azimuth 
considered the map is shifted to compensate for 
the centering error, and the corrected range scale 
is used to lay off distance. 

156 THE CALCULATION 

OF VERTICAL COVERAGE 

15,6,1 Introduction 

The computation of vertical coverage diagrams in 
the optical region consists essentially of adding two 
vectors, the contributions of the direct and reflected 
waves, which have been modified by earth curva¬ 
ture, antenna directivity, etc. The actual computa¬ 
tion of the contours of constant field strength tends 
to be laborious because of the implicit nature of the 
parameters. The problem may be formulated in a 
rigorous, general manner, but the solution is likely 
to be unwieldy. 

For field purposes where high accuracy is not 
required, a method of computing vertical lobe 
patterns is desired that is direct, does not require 
excessive calculations, provides a simple physical 
interpretation of terrain effects, and is flexible. The 
methods presented here are designed to meet these 
requirements, and the computer may readily accom¬ 
modate the labor of calculations to the required 
accuracy and the complexity of the problem. 

The path difference of the direct and reflected 
rays, the distance of the reflection point, and the 
vertical angle are functions of each other, while the 
reflection coefficient, the divergence factor, and other 
factors depend on the vertical angle. It is therefore 
desirable to examine the problem in a general way 
to determine what simplifications may be introduced. 

With microwaves the reflecting surface must be 
quite smooth to be effective. Thus by equation (16) 
for the S band and an angle of 1 degree the roughness 
must be less than 15 in. if the reflection is to be of 
much assistance. The rolling character of sea waves 
makes a substantial variation in signal strength so 
that the reliable range is only skghtly greater than 
that of the direct wave alone. Also highly directive 
antennas are commonly used with microwave radars. 
These factors reduce the magnitude of the interfer¬ 
ence effects. The fineness of the structure of a micro- 
wave pattern and the relatively weak reflection 
effects commonly encountered therefore render it a 
useful approximation to deal with the direct wave 
pattern only for most purposes. 




ALTITUDE IN FEET 


146 


SITING AND COVERAGE OF GROUND RADARS 


Fire control and searchlight radars normally 
operate at high angles so that they also are mainly 
concerned with the direct wave. The GCI and other 
low-sited radars have their reflection areas within a 
mile of the antenna so that earth curvature may be 
ignored, which means a considerable simplification. 
The case which requires the most careful considera¬ 
tion is early warning, VHF, high-sited radar which 
is dependent on the reflected wave for much of its 
performance. A careful analysis of all factors involved 
is therefore usually required. Prepared diagrams for 
various heights and wavelengths must be considered 
carefully before being used, as local terrain features 
may radically alter the lobe pattern. 

The accuracy and detail desired and the type of 
site influence the amount of calculation involved. 
With a low-sited VHF radar only a few lobes are 
formed so that the shape and location of the lobes 
is of interest. With a high-sited VHF radar the lobes 
are numerous and the gaps are small so that there 
is little likelihood of losing a target in a null area or 
of being able to associate an echo with a particular 
lobe. In this case the envelope of the lobes is of 
particular interest. 

The high-power microwave radars are best suited 
for vital areas with high traffic density. However, 
for most purposes the basic long-range, early warning 


radars used by the ground forces operate in the VHF 
band. They are normally sited high, that is several 
hundred feet and up, in order to secure low lobe 
angles and numerous lobes. The need for good rein¬ 
forcement and tactical considerations lead to the 
use of the sea as a reflecting surface where feasible. 
The general high-sited radar problem will be ana¬ 
lyzed in detail, and the use of approximate, simplified 
methods of calculation will be described where 
applicable. 

15.6.2 The Vertical Coverage Diagram 

The object of test flights and field intensity 
calculations is the construction of the vertical cover¬ 
age diagram. A typical diagram for a long-range, 
early warning, VHF radar is shown in Figure 46. 
The contours or lobes on this diagram represent the 
locus of all points in space along a particular azimuth 
where an incoming plane of standard type, usually 
a twin engine medium bomber, will produce a mini¬ 
mum detectable signal. A minimum detectable signal 
is ordinarily taken to be one that has a signal-to-noise 
ratio of unity. This may also be expressed in other 
terms such as field intensity or voltage at the 
receiver terminals. For other types of planes, or a 
number of planes, or different aspects of the same 
plane, the lobe pattern has a different size. 



Figure 46. Vertical lobe diagram. 
















































THE CALCULATION OF VERTICAL COVERAGE 


147 


It will be noted that the vertical scale is nearly 
10 times as great as the horizontal scale, causing a 
marked distortion in angles and crowding of angles 
above 10 degrees. The lines of constant altitude are 
parabolas, owing to the curvature of the earth. Their 
shape is given by the equation 


y = h - 


d 2 - 5,280 
2 ka 


(48) 


Here y = the ordinate measured from the horizontal 
line through zero; 

h = the height of the curve at zero range, in 
feet; 

d = distance along the earth in miles; 
a = radius of the earth in miles; 
ka = equivalent earth radius. 



For standard conditions k is taken as %. At 40° 
latitude the radius of the earth is 3,960 miles. Sub¬ 
stituting in equation (48) gives the convenient 
relation: 

y = h , (49) 

with y and h in feet, and d in miles. 

Thus in Figure 46 a medium bomber coming in 
at 5,000 ft would first be detected at 108 miles, the 
signal would increase in strength, reaching a maxi¬ 
mum around 96 miles, and then decrease and be lost 
at 84 miles. In the null region between 84 and 77 
miles there would be no detection. Similar regions 
of detection and nulls would be encountered as the 
plane came in closer. The nulls do not come into 
the origin when the direct and reflected rays are 
unequal. This gap filling is secured at the price of 
shorter lobes. Above 3 degrees the lobes cannot be 
distinguished from the nulls. 

Only lobes due to the main free space lobe of the 
antenna pattern are ordinarily plotted, as targets 


higher than about 10 degrees are of little interest 
to an early warning radar. Because most detection 
occurs at angles under 2 or 3 degrees, no distinction 
will be made between slant range and horizontal 
range. 

The calculation of the coverage diagram will be 
approached in successive steps. The first step will 
consist of calculation of the angular position of the 
lobe maxima and minima. This will be done in three 
different degrees of approximation corresponding to 
different situations encountered in practice. The next 
step is the calculation of the length and shape of 
the lobes themselves, which is given in a later section. 


lo6 3 Flat Earth Lobe Angle Calculations 

When the reflection point is so close that earth 
curvature may be ignored, the rays may be drawn 
as in Figure 47. The transmitter T has the center 
of the antenna at height hi above the horizontal 
reflecting surface. The antenna is assumed t'o have 
horizontal polarization; that is, the dipoles are 
parallel to the reflecting plane and perpendicular 
to the direct ray r d . The target height is h 2 . Both hi 
and h 2 are several wavelengths or more, and r d is so 
large that the field at the target falls off as l/r d . 
The image of the antenna is at T' at a distance hi 
below the reflector. The length of the ray from 
T' is r. 

The coefficient of reflection is p, and the phase lag 
at reflection is </>. The electric field strength due to 
the combined direct and reflected waves ( r d ~ r) 
may be written as 

E = 1 -J- p 2 -f" 2 p cos (</> T 8) (66) 


where 5 = 2i r— = phase lag due to the path differ- 
X 

ence, 

A = r — r d = path difference of the direct 
and reflected rays, 

Ei = the field strength at unit distance. 


For horizontal polarization and small angles p is 
unity and <f> is 180 degrees and equation (50) reduces 
to 


E 



8 


2Ei . ttA 


= -sin — . 

r X 


(51) 










148 


SITING AND COVERAGE OF GROUND RADARS 


In the construction of a vertical coverage diagram 
it is important to be able to draw the lines of constant 
path difference. Of special interest are the lines of 
maxima in the center of the lobes and the lines of 
minima or nulls. These lines correspond to 

A = r — Td = constant . (52) 

For the case of a flat earth these lines are by defini¬ 
tion confocal hyperbolae with T and T' as foci and 
A as the major axis. This is shown in Figure 48 for 
a target at short range. In a typical case 0 will be 



positive and approximately equal to y. From 
geometry 


r d 


4 hS - A 2 
2A — 4/ii sin 0 ’ 


(53) 


When rd is very large compared with hi the angle 
7 is equal to (3, and the denominator of equation (53) 
is practically zero, giving 

sin 7 = ^ • (54) 


Using equation (51) with the (irA)/X = t/2, the 
lobe maxima are given by 


A = 



(55) 


where n = 1, 3, 5 • • • . Minima are given by values 


of n = 0, 2, 4, 6, • • • . 

Substituting in equation (54) 


si 1^ 

II 

c*- 

‘35 

(56) 

or to a sufficient approximation 


Si I’rfi 

II 

(57) 


Here y = the angle of elevation of the target referred 
to the horizontal at the ground below the 
antenna, in radians; 


n = number of half-wavelengths difference 
between the direct and indirect paths. 
n — 1, 3, 5, etc., for maxima of lobe 
number 1, 2, 3, • ♦ • (n + l)/2 counting 
from the reflector up. n = 0, 2, 4, 6, etc., 
for minima of null numbers 1, 2, 3, 4, 
•••(» + 2 )/ 2 ; 

hi = the height of the center of the antenna 
above the reflector; 

X = wavelength; 
with hi and X in the same units. 

From Figure 47 it follows that d h the distance to 
the reflection point, is given by 

, _ _A_ 

dl tan * ’ 


or taking tan 'k = sin = 7 (which may be done 
provided di is small enough compared to d 2 and large 
compared to hi) and substituting in equation (57), 


di 


4/i 1 2 
n\ 


(58) 


Here d h hi, and X must be expressed in the same units* 
For high sites and distant targets the angle 7 
becomes smaller, and the approximation involved 
in equations (57) and (58) requiring di to be small 
compared to d 2 becomes worse. In Table 4 are listed 
the minimum values that n\ may have for an error 
of 1 per cent or less in equation (57) at different 
antenna heights. Also is given the minimum value 


Table 4. One per cent error in 7. 


h h ft 

Minimum 7° 

Minimum nX, ft 

400 

1.5 

43 

200 

1.1 

15 

100 

0.8 

6 

50 

0.6 

2 

15 

0.3 

0.3 


of 7 corresponding to n\. Thus equation (57) when 
used on a 100-ft site at 100 me (X = 9.84 ft) will 
give values which are in error by less than 1 per cent 
for all lobes and for angles above 0.8 degree. If the 
100-ft site operated at 1,000 me (X = 0.98 ft) the 
minimum value of n would be 6 corresponding to 
the fourth null. The error in 7 is always positive 
and increases rapidly with antenna height, and at 
a height of 1,000 ft and a frequency of 100 me the 
formula is incorrect for all angles of interest. At 
















THE CALCULATION OF VERTICAL COVERAGE 


149 


distances such that the earth curvature drop is 
comparable to hi, equation (57) does not even give 
the correct order of magnitude for 7 . 

Examples 9 and 10. Flat Earth Lobe Angle Compu¬ 
tations. Lobe angles for two cases will be computed, 
Example 9, a 200-mc set at 15 ft and Example 10, 
a 500-mc set at 50 ft. 


Example 9 

OAf) 

x = fsi x 3 - 28 = 4 - 92ft 


For n = 1 (first lobe) 

= 1 X 4.92 
4 X 15 

, 4 X (15) 2 

(l l = - 

1 X 4.92 


X 57.3 = 4.7 C 


= 183 ft 


Example 10 
X = 1.97 ft 

7 = 0.564° 
di = 5,080 ft 


Table 5. Lobe angle and distance to reflection point. 


n 

Example 9 

7, degrees d\, ft 

Example 10 

7, degrees d\, ft 

1 (lobe 1) 

4.7 

183.0 

0.56 

5080 

2 (null 2) 

9.4 

91.5 

1.13 

2540 

3 (lobe 2) 

14.1 

61.0 

1.69 

1693 

4 (null 3) 

18.8 

45.7 

2.26 

1270 

5 (lobe 3) 

23.5 

36.6 

2.82 

1016 


In practice some of the lobes listed for Example 9 
may be absent because of nulls in the antenna 
pattern. The angle listed for the first lobe of Example 
10 is slightly over 1 per cent too large. 


Lobe Angles Corrected 
for Standard Earth Curvature 

Equation (57) may be modified to include the 
effect of earth curvature approximately and to give 
the lobe angles for the majority of sites with accept¬ 
able accuracy. 

For antennas several hundred or more feet high, 
di as given by equation (58) may be large enough 
so that the earth curvature drop is appreciable. 
In Figure 49 is shown a transmitter of height hi 
above the horizontal plane GH. The radius of the 
standard earth is ka. At D, the center of the reflection 
area for the lobe considered, is drawn a tangent 
plane CDE, which intersects hi at a distance h\ 
below the center of the antenna and which will be 
considered the equivalent antenna height. This then 
is the part of hi which determines the angle 7 ' 
which the lobe center line CL makes with the tangent 
plane CDE. Subtracting from 7 ' the angle 6 which 



Figure 49. Lobe angles corrected for earth curvature. 


the tangent plane CDE makes with the horizontal 
at the base of the antenna GH, the lobe angle 7 
referred to the horizontal at the antenna is obtained. 
From equation (49) it follows that 

lh' = hy - ^ . (59) 


Here hi and hi are expressed in feet, di in miles, and 
k is assumed to be %. 

This height hi is the portion of hi that is effective 
in connection with the plane CDE and when substi¬ 
tuted in equation (57) gives the angle 7 '. 



Since the earth’s radius ka is perpendicular to GH and 
CDE, the tangent angle is 6. It is always negative: 


di _ di 

ha ~ 5,280 ’ 


(61) 



di 

5,280 ‘ 


(62) 


n is an odd integer for lobe maxima and an even 
integer for lobe minima, hi in feet, di in miles. 

The value of di to substitute in equation (62) 
must also satisfy equation (58). A convenient method 
of solving these equations is to plot a curve of 
equation (59) and also of equation (58) in the form 


4 (hi f ) 
5,280diA ' 


Corresponding values of hi and di for the desired 
value of n are then substituted in equation (62). 

While equation (62) is subject to the same sort 
of limitation as equation (57), it will be noted that 



















150 


SITING AND COVERAGE OF GROUND RADARS 


in the region of greatest interest, that is, small 
angles, hi is itself small, and this tends to compen¬ 
sate the error. The modifications introduced permit 
the use of the simple plane earth formulas, since for 
a particular angle the tangent plane is taken as the 
reflection surface. 

The angle y given by equation (62) is the trans¬ 
formed angle to be used in constructing the vertical 
coverage diagram based on a modified earth radius 
of ka = 5,280 miles. If the true angle is desired, the 
true earth radius a = 3,960 miles must be used in 
equation (62) instead of 5,280 miles. 

Examples 11 and 12. Lobe Angles Corrected for 
Earth Curvature. Lobe angles will be computed by 
this method for two radar sites. 


Example 11 

hi = 500 ft 
/ = 200 me 

From equation (59) 

hi' = 500 - ~ 


Example 12 

hi = 3,000 ft 
/ = 100 me 


ht' = 3,000 - — 
2 



Table 6. Lobe angles for radar. (Example 11.) 


From Figures 

50 and 51. 

Equation (60) 

7' = 1.23 ~ 

hi 

Equation (61) 

e - - dl 

Equation (62) 

t = y + o 

Equation (57) 

n 

/y _ _ 

5,280 

4 hi 

n 

hi' 

di 

radians 

radians 

radians 

degrees 

radians 

0 

0 

31.6 

0 

-.005983 

-.005983 

-0°20'22" 

0 

1 

34F.5 

17.8 

.003602 

-.003372 

+ .000230 

+0° 0'47" 

.00246 

2 

414.0 

13.1 

.005943 

-.002481 

.003462 

0°11'54" 

.00492 

3 

448.0 

10.2 

.008238 

-.001932 

.006306 

0°21'39" 

.00739 

4 

464.6 

8.4 

.010592 

-.001591 

.009001 

0°30'56" 

.00985 

5 

475.5 

7.0 

.01294 

-.001326 

.01161 

0°39'54" 

.0123 

6 

481.4 

6.1 

.01532 

-.001155 

.01417 

0°48'43" 

.0148 

7 

486.0 

5.3 

.01772 

-.001004 

.01672 

0°67'29" 

.0172 

8 

489.0 

4.7 

.02011 

-.000890 

.01922 

1° 6' 4" 

.0197 

9 

491.6 

4.1 

.02252 

-.000776 

.02174 

1°14'45" 

.0221 

10 

493.2 

3.7 

.02493 

-.000701 

.02423 

1°23'19" 

.0246 

11 

494.6 

3.3 

.02734 

-.000625 

.02672 

1°31'55" 

.0271 

12 

495.5 

3.0 

.02978 

-.000568 

.02921 

1°40'26" 

.0295 

13 

496.1 

2.8 

.03222 

-.000530 

.03169 

1°48'58" 

.0320 

14 

496.6 

2.6 

.03468 

-.000492 

.03419 

1°57'33" 

.0345 

15 

497.1 

2.4 

.03720 

-.000454 

.03675 

2° 6'23" 

.0369 

16 

497.4 

2.3 

.03955 

-.000436 

.03911 

2°14'30" 

.0394 

17 

497.6 

2.2 

.0420 

-.000417 

.0416 

2°23' 2" 

.0418 

18 

497.8 

2.1 

.0445 

-.000398 

.0441 

2°31'44" 

.0444 

19 

498.0 

2.0 

.0469 

-.000379 

.0465 

2°39'54" 

.0468 

20 

498.2 

1.9 

.0494 

-.000360 

.0490 

2°48'30" 

.0492 

21 

498.4 

1.8 

.0518 

-.000341 

.0515 

2°57' 8" 

.0517 

22 

498.6 

1.7 

.0542 

-.000322 

.0539 

3° 5'22" 

.0541 

23 

498.8 

1.6 

.0567 

-.000303 

.0564 

3°14' 0" 

.0567 













































THE CALCULATION OF VERTICAL COVERAGE 




151 


Table 7. Lobe angles for radar. (Example 12.) 


From Figures 

50 and 51 

Equation (60) 

y' = 2.46 ~ 
hi 

Equation (61) 

o dl 

Equation (62) 

T = 7' + 6 

Equation (57) 

n 

7 = 4 h 

5,280 

n 

W 

di 

radians 

radians 

radians 

degrees 

radians 

0 

0 

77.4 

0 

-.01466 

-.01466 

—0°50'24" 

0 

1 

930 

64.3 

.002645 

-.01218 

-.00954 

—0°32'49" 

.00082 

2 

1245 

59.2 

.003952 

-.01121 

-.00726 

—0°25' 0" 

.00164 

3 

1458 

55.5 

.005063 

-.01051 

-.00545 

—0°18'44" 

.00246 

4 

1638 

52.2 

.006007 

-.00989 

-.00388 

—0°13'20" 

.00328 

5 

1788 

49.2 

.006880 

-.00932 

-.00244 

-0° 8'22" 

.00410 

6 

1910 

46.7 

.007730 

-.00885 

-.00112 

-0° 3'52" 

.00492 

7 

2013 

44.4 

.008550 

-.00841 

+.00014 

+0° 0'29" 

.00574 

8 

2108 

42.4 

.009335 

-.00803 

.00130 

0° 4'28" 

.00656 

9 

2195 

40.6 

.01018 

-.00769 

.00249 

0° 8'33" 

.00738 

10 

2246 

38.8 

.01095 

-.00735 

.00360 

0°12'22" 

.00820 

11 

2308 

37.2 

.01173 

-.00705 

.00468 

0° 16' 6" 

.00902 

12 

2359 

35.8 

.01251 

-.00678 

.00573 

0° 19'41" 

.00984 

13 

2408 

34.4 

.01328 

-.00651 

.00677 

0°23'16" 

.01066 

14 

2452 

33.1 

.01404 

-.00627 

.00777 

0°26'44" 

.01148 

15 

2488 

32.0 

.01484 

-.00606 

.00878 

0°30'10" 

.01230 

16 

2525 

30.8 

.01558 

-.00583 

.00975 

0°33'31" 

.01312 

17 

2559 

29.7 

.01635 

-.00562 

.01073 

0°36'50" 

.01394 

18 

2588 

28.7 

.01712 

-.00544 

.01168 

0°40' 8" 

.01476 

19 

2623 

27.8 

.01782 

-.00526 

.01256 

0°43'10" 

.01558 

20 

2638 

26.9 

.01866 

-.00509 

.01357 

0°46'40" 

.01640 

21 

2662 

26.0 

.01940 

-.00492 

.01448 

0°49'48" 

.01722 

22 

2685 

25.1 

.02030 

-.00475 

.01555 

0 o 53'26" 

.01804 

23 

2702 

24.4 

.02093 

-.00462 

.01631 

0°56' 4" 

.01860 


These equations are plotted in Figure 50. From 
equation (63): 


n 


5,280 X 4.92 X d x 


n = 0.000077 


M: 

di 



Reading values of hi and di from Figure 50 and sub¬ 
stituting in the above equations, curves of n and* di 
are plotted in Figure 51. From these two curves 
may be read the values of hi and di corresponding 
to integral values of n» The calculation of y' and 6 
from equations (60) and (61) are conveniently per¬ 
formed by arranging columns as shown in Tables 
6 and 7. 

For purposes of comparison with equation (62) 
the last column gives values of y computed by means 
of equation (57). In Table 6 the error in the figures 
computed from equation (57) is seen to be consider¬ 
ably below n = 10; for higher values of n the two 
formulas tend to show fair agreement. In Table 7 
the disagreement is marked even at n — 23 indicat¬ 
ing that equation (57) is unsuitable for high sites. 

The lobe angles are shown in Figures 52 and 53. 
The lines of constant altitude over the modified 
earth are plotted from equation (49). The lobe 
angles are constructed by drawing radial lines from 
the center of the antenna, while the height in feet 
at a given distance is obtained by multiplying y 
(in radians) by 5,280 times this distance in miles. 
The lines have not been drawn close in because of 
the crowding and because they actually start near 


Figure 51. Reflection area graph. 






































































152 


SITING AND COVERAGE OF GROUND RADARS 



Figure 52. Lobe angles for Example 11. 


the origin rather than at the center of the antenna. 

The error in the position of the center lines of the 
lobes near the antenna is a limitation on this method; 
but this occurs in a region which, because of gap 
filling, has no nulls and is therefore of little concern. 
Another difficulty is that the lower lobes are actually 
curved instead of straight; but as long as the site is 
not too high, say under 100 ft (100 me), the curva¬ 
ture is small and unimportant. In general the method 
of equation (62) gives reasonably correct lobe angles 
for most high sites and with a moderate amount of 
computation. This is the first step in the preparation 
of the coverage diagram. Later sections will discuss 
construction of lobes about these center lines. 

io.6.o The General Lobe Angle Formula 

For very high sites (over 1,000 ft) and frequencies 
over 200 me, it is desirable to have a more accurate 
expression for the locus of constant path difference 
than is afforded by straight lines. This is of especial 
interest in the first few lobes as these determine the 


low coverage which is of great tactical importance. 
The method described here overcomes the limitations 
of equation (62) and may be used for the highest sites. 

In Figure 54 is shown the antenna above a curved 
reflecting surface whose radius is taken as % of the 
earth’s radius to allow for atmospheric refraction. 
The tangent plane CE makes an angle 0 with the 
horizontal at the antenna, and 0 is given by — ( di/ka) 
as shown in Figure 49. 

hi = height of the center of the antenna above 
the earth’s surface, in feet. 

W = equivalent height of the antenna, in feet 
— equation (59). 

r d = distance from the antenna to the target, in 
miles. 

A = distance from the antenna to the reflection 
point, in miles. 

B = distance from the reflection point to the 
target, in miles. 

A = path difference, A + B — r d , in miles. 

X = wavelength, in feet. 

































THE CALCULATION OF VERTICAL COVERAGE 


153 



Figure 53. Lobe angles for Example 12. 


0 = angle between the tangent plane CE and the 
horizontal at the antenna, in radians. This 
angle is always negative. 
ka = radius of the modified earth, 5,280 miles. 

= angle between the direct ray r d and the 
horizontal plane CE, in radians. 

= angle between the reflected ray A or B and 
the horizontal plane CE, in radians. 
n — number of half-wavelengths path difference. 

In the triangle ABr d (cosine law) 

r d = VA 2 + B 2 + 2 AB cos 24^ . (64) 

From the definition of path difference: 

A = A + B - r d = 2 x 5 28 O ’ ^ 

A + B — A = \/A 2 + B 2 + 2 AB cos 24^ ; 
squaring and dropping terms that cancel out gives 
2 AB - 2 AB cos 2* - 2BA = 2AA - A 2 , 


or solving with respect to B, 


B = 


AA - hA 2 


A(1 - cos 2^) - A 


( 66 ) 


Substituting 


A = 


n\ 


2 X 5,280 ’ 
into equation ( 66 ) gives 


n\ 


B = 


10,560 


1 / nX V 

2 \ 10,560/ 


A(1 — cos 24') — 


nX 


10,560 


(67) 


Several approximations will be introduced to 
simplify equation (67): 

A will be taken to equal di since is of the order 
of 3° or less. 

From Figure 54 it follows that sin 4' = /q'/5,280A, 
or for small angles, 4^ = hi /5,280A. 

Substituting for hi [equation (59)] it follows that 


hi — \ ch 2 
5,280 d 


(68) 


Using the approximation 

cos 24' = 1 — 24' 2 , 












































154 


SITING AND COVERAGE OF GROUND RADARS 



and neglecting \(n\/ 10,560) compared to A, equa¬ 
tion (67) becomes 


nX 


B = 


10,560 


-di 


2di* 2 


n\ 


10,560 

From the law of sines 

sin 2^ _ sin Qfr + 4^) _ sin 
r d ~ B ~ i 

sin (¥ + 4^) = 

When 4' and 4> d are small 


B sin 24^ 

Td 


D 

y + y d = - 2 * 
r d 


and 


4^) 


(69) 


4> — 4^ = — 24> , 
r d 


and hence by subtraction 

T B ~ A , 

4^ = -4' . 

r d 

Since 4' is a small quantity r d may be taken to equal 
A + B, and A = d h that is 


B - di _ 


(70) 


This is the angle of the target with respect to the 
tangent plane CE as seen from the antenna. The 


angle desired however is y, which is measured with 
respect to the horizontal at the antenna, GH. As 
shown in Figure 54 

T = 4^ ~b 0 . 

From equation (61) 



The line of minimum path difference (A = 0) is 
along the earth’s surface from the transmitter to 
the horizon, and beyond it is along the line of sight 
tangential to the horizon since the direct and indirect 
waves are equal in that case. Maximum path differ¬ 
ence occurs directly below the antenna and is equal 
to 2 hi. Since the path difference is also nX/2, the 
maximum value of n is 4 h\/\. In practice the vertical 
directivity of the antenna limits n to a much smaller 
value. 

Consider a wave which is reflected from directly 
under the antenna, and let ho denote the height 
above the reflector at which the path difference is 
n\/2. Then 

hi + ho — (h\ — ho) = 2 > 

or 

ho = f. (71) 

Thus if X is 10 ft the center of the first lobe will be 
2.5 ft high at zero range. For most purposes the lobes 
and nulls may therefore be considered to start at 
the origin. 



















THE CALCULATION OF VERTICAL COVERAGE 


155 


To use this method it is best to arrange the calcu¬ 
lations in a tabular form. Points along the lobe center 
are selected by using various values of di for the 
value of n desired. Next 'k is obtained from equation 
( 68 ) and substituted in equation (69), and B and 
'k are substituted in equation (70) yielding which 
is combined with 6 to obtain 7 . The curve of constant 
path difference is then plotted from 7 and r d , which 
are now known. 

Example 13. The General Lobe Angle Formula. To 
illustrate this method a radar 3,000 ft high and 
operating at 100 me will be used. A trial value of 
60 miles is arbitrarily selected for d\ and substituted 
in equation ( 68 ), giving 


3,000 - jX (60) 2 
' 5,280 X 60 


0.003788 radian . 


In equation (69) using n — 1 and X = 9.84 ft, 



1 X 9.84 
10,560 


X 60 


1 \/ q 04 

2 X 60(0.003788) 2 - 


70.85 miles. 




70.85 - 60 
70.85 + 60 X 


0.003788 = 0.000314 radian . 


6 = — - ■ ■ = —0.01136 radian . 

5,z8U 

7 = 0.000314 - 0.01136 = -0.01105 radian . 
r d = 60 + 70.85 = 130.85 miles . 

Laying out the angle 7 from the antenna and 
marking off the distance r d gives one point on the 
curve of constant path difference. Enough other 


points are computed to enable one to draw a smooth 
curve. The computations may be arranged as shown 
in Table 8 . The values selected for should be 
small enough so that the denominator of equation 
(69) is positive. 

These two curves are plotted in Figure 55. For 
comparison is shown the first lobe as computed from 
equation (62), and it can be seen that this equation 
may lead to appreciable error in estimating low 
coverage. For most purposes it will suffice to calcu¬ 
late lobes higher than the first one or two by means 
of equation (62). 

15.6 6 The Calculation of Lobes 

Three methods of computing lobe angles were 
given corresponding to low, medium, and high sites, 
in order to relate the labor of the computations to 
the complexity of the problem. A similar procedure 
will be followed in the calculation of the lobe shapes. 

The lobe diagram represents the locus of all points 
along a particular azimuth of a definite field intensity, 
usually the threshold of detection. If the site has 
horizontal symmetry throughout its sector of opera¬ 
tion one diagram will suffice. Usually several dia¬ 
grams are required, and it is common practice to 
prepare a diagram for the central azimuth of the 
sector and for 10 degrees inside of each limit of scan. 


15 6 7 Low Site Lobes 

The electric field intensity at the target is the 
resultant of the direct and reflected waves which 
have the same amplitude and a phase angle which 
varies continually as the lobe angle 7 is increased. 


Table 8. General lobe angle formula. (Example 13.) 


di, 

miles 

radians 

B, 

miles 

*d, 

radians 

- 0 , 
radians 

-T, 

radians 

rd, 

miles 

(n = 1) 65 

.002800 

696.0 

.0023220 

.0123105 

.00999 

761.0 

62 

.003290 

141.2 

.0012810 

.0117450 

.01046 

203.2 

60 

.003788 

70.85 

.0003140 

.0113636 

.01105 

130.85 

58 

.004300 

44.60 

-.0005618 

.0109850 

.01155 

102.60 

55 

.005118 

26.32 

-.0018050 

.0104166 

.01222 

81.32 

50 

.006628 

13.45 

-.0038380 

.0094698 

.01331 

63.45 

30 

.016090 

1.91 

-.0141600 

.0056820 

.01984 

31.91 

(n = 2 ) 60 

.003788 



.0113636 



58 

.004300 

386.0 

.0031770 

.0109850 

.007808 

440.0 

56 

.004840 

137.5 

.0020390 

.0106060 

.008567 

193.5 

55 

.005118 

101.0 

.0015090 

.0104166 

.008908 

156.0 

53 

.005700 

62.6 

.0004733 

.0100381 

.009565 

115.6 

50 

.006628 

36.78 

-.0010115 

.0094698 

.010480 

86.78 

30 

.016090 

4.09 

-.0122300 

.0056820 

.017910 

34.09 



















156 


SITING AND COVERAGE OF GROUND RADARS 



Figure 55. Lobe and null lines. (Example 13.) 


For a perfect reflector and horizontal polarization 
the phase lag is equal to + 7 r + (2 w/\) X (nX/2) 
which adds up to mr + tt. Odd integral values of 
n give lobe maxima, and intermediate values give 
other points on the lobes. 

The sum of the two vectors practically parallel 
and of equal magnitude, Ei/d, is 

E = ^ cos [(» + 1) , (72) 

where Ei is the electric intensity (microvolts per 
meter) in the equatorial plane 1 mile from the 
antenna in free space, that is, without a reflecting 
surface. E is the electric intensity at the point 
considered in microvolts per meter, d is the distance 
to the point, in miles, n is a number related to the 
angle of elevation. It is an odd integer for lobe 
maximums and an even integer for nulls. For a 
given antenna and radar the electric intensity E 
will produce at the input of the receiver a voltage, 

v 2 = ^ sin (90°n) , (73) 

where ki is a proportionality factor for the voltage 
applied to the receiver input. If V 2 is set equal to 
the minimum operating voltage of the receiver 
equation (73) becomes 

d = sin (90°n) . 

' min 

The term kiEi/V mln is usually obtained from test 


flights on the particular radar or on radars of the 
same type. The usual form is 

d = dmax sin (90°n) , (74) 

where d max stands for kiEi/V min and is a measure 
of the performance of the radar set. 

The lobes will be polar sinusoids and the minima 
will go to zero only when the amplitude of the direct 
and indirect waves are equal. These conditions will 
not obtain if the vertical directivity of the antenna 
affects the rays unequally, if the reflected wave 
suffers imperfect reflection or divergence, or the 
atmosphere or terrain has unequal effects on the 
two waves. Low sites are generally free from the 
above effects and equation (74) may be used with 
acceptable accuracy. 

Example 14 . Low Site Lobes. A radar operating on 
200 me is 25 ft high and has a maximum range of 
60 miles. The lobes occur at 2.82°, 8.46°, and 14.1° 
and the nulls at 0°, 5.64°, 11.28°. The method of 
plotting a lobe is shown in Figure 56. n may be 
divided into as many parts as desired, and the 
corresponding range for each obtained from equa¬ 
tion (74). Thus at n = 0.7 the angle is 

° ! X t 92 = 0.0344 radian , 

4 X 2o 

d = 60 sin (90° X 0.7) = 53.46 miles. 

A line is drawn at this angle, and a point is marked 
off at a range of 53.46 miles. 










ALTITUDE IN FEET 


THE CALCULATION OF VERTICAL COVERAGE 


157 



Figure 56. Low site lobes. (Example 14.) 

















































158 


SITING AND COVERAGE OF GROUND RADARS 


15 6 8 Lobe Diagrams of Medium Height Sites 

In dealing with radars at medium heights, say 
from 100 to 1,000 ft, a more involved treatment is 
required, owing to earth curvature effects. The 
procedure followed in this section is to compute a 
value of d max for each lobe from which a sinusoid 
is constructed at the angle of the lobe. The envelope 
of the lobes is considered to be of principal interest, 
the lobe shape being of secondary importance. 

The strength of a wave is measured in miles, that 
is, the distance at which the standard target must 
be to give a standard signal response such as a 
signal-to-noise ratio of one. The distances corres¬ 
ponding to the direct and reflected waves are added 
to get lobe maxima and subtracted to get minima. 
The direct and reflected waves will therefore be 
computed separately. The phase shift due to reflec¬ 
tion will be taken as 180°, and the phase shift due 
to other causes than path difference will be considered 
negligible. This assumption greatly simplifies calcu¬ 
lations and is a good approximation for small angles 
and horizontal polarization. For vertical polariza¬ 
tion, especially in the YHF band, it is a poor 
approximation. 

The direct wave is affected only by the modified 
antenna pattern. The reflected wave is affected by: 

1. Shoreline diffraction. 

2. The modified antenna pattern. 

3. Earth curvature. 

4. Coefficient of reflection. 

5. Divergence. 

Terrain effects such as reflection areas of limited 
extent, the shoreline, cliff edges, and obstacles involve 
diffraction. A simple, flexible method for solving such 
problems will be developed in the next section. 


156 9 Shoreline Diffraction 

Unfortunately sites of sufficient height are 
frequently some distance inland, and a considerable 
portion of the reflection surface is on land. The 
poor reflecting qualities of land, especially when 
rough, causes the high angle lobes due to nearby 
reflection to be reduced as much as 50 per cent in 
length. This is a common cause of poor high coverage 
so often experienced in field installations and the 
inability to detect high-level bombing attacks except 
at perhaps 10-mile ranges. In this section will be 
developed a method of computing the vertical 
coverage pattern for the typical high site with part 
land and part sea reflecting surfaces. 

In most cases the profile of the land between the 
transmitter and the shore will be found to be too 
rough for coherent reflection, as may be determined 
from equation (16). If substantial regular areas or 
obstacles occur between the antenna and the shore 
line they should be treated as described in Section 
15.6.12, on the modified antenna pattern. 

15610 Sea Reflection 

with Diffuse Land Reflection 

The problem treated in this section will be that 
shown in Figure 57. The land in the foreground is 
so rough as to cause only diffuse reflection, and no 
regular areas exist which will affect the vertical 
pattern below 15°. 

The diffuse reflection from the land area has a 
random phase relation, and the field intensity in a 
particular direction is relatively small. The effect of 
the land reflection on the interference pattern is 



Figure 57. Fresnel zones on land and sea areas. 










THE CALCULATION OF VERTICAL COVERAGE 


159 


therefore neglected. This is equivalent to termination 
of the reflecting surface at the shore line. 

In order to describe diffraction at a shore line a 
system of Fresnel zones for each lobe is considered 
to be formed on the sea with the reflection point of 
the lobe as their center. The zones will be ellipses 
because of the inclination of the rays. The influence 
of the shore line will be determined by the number 
of zones which are not interfered with by the shore. 

Thus a low angle lobe which has its central Fresnel 
zone far out to sea would be virtually unaffected by 
the limited reflection area, as numerous zones are 
formed on the sea. This is indicated by A in Figure 
57, which represents the reflected wave. At B, a 
higher angle lobe, there are only two zones intact, 
and the reflected wave is weak. Had only one zone 
been complete, the reflected wave would have been 
stronger than A. At C only portions of outer zones 
are formed on the sea, and the reflected wave is 
negligible. 

The effect of the reflecting surface may be repre¬ 
sented by an image antenna located in the earth 
under the radar antenna at a depth hi below the 


surface as in Figure 58. The nonreflecting land surface 
then acts precisely as a straight diffracting edge for 
the image antenna and indirect ray. A general 
formula will be developed which gives the situation 
of any Fresnel zone of any lobe for a given radar 
station. From this formula and the distance to the 
shoreline it may be determined for each lobe which 
zone is intercepted by the shore. In the graph in 
Figure 58 is plotted the relative intensity of the 
reflected ray as a function of m, the number of the 
zone touching the shore. In the illuminated region 
at large angles, as A, the relative intensity is close 
to unity. Approaching the shore it oscillates about 
unity, reaching a maximum of 1.18. In the shadow 
region, the intensity drops to low values. Thus, 
knowing m, the effect of shoreline diffraction on the 
reflected ray may be obtained. The derivation will 
be developed for a plane reflecting surface, since, as 
it has been shown in Section 15.6.4, for lobe angles 
corrected for standard earth curvature, the effect of 
earth curvature may be taken into account by using 
hi [equation (59)] instead of hi. In most cases di will 
be small and hi may be used with little error. 



IMAGE ANTENNA 


Figure 58. Shore line diffraction. 














160 


SITING AND COVERAGE OF GROUND RADARS 


15 611 General Formula 

for the Reflection Area 

In Figure 59 is shown an image antenna T" sending 
radiation through a plane of indefinite extent. In 



Figure 59. Fresnel zones on the reflecting surface. 


In Figure 59 is shown the first Fresnel zone for an 
angle F with a corresponding value of n. Ray 2 
passes through the center of the first zone and rays 
1 and 3 pass through the near and far edges respec¬ 
tively. Because of the great distance of the target 
the rays 1, 2, and 3 are parallel. 

For the first zone the path difference between 1 
and 2 is X/2. For zone m the path difference is 
raX/2 (where m = 1, 2, 3, etc.). Since the points 
di and d n are not equidistant from the target, the 
distance Xi cos F must be subtracted from ray 2 to 
compensate for the increased path length of ray 1 
above the plane. 

raX 7 l hi _ \ 

— = Zi — -—7 — Xi cos F . 

2 \sin F / 

In the right triangle 

2 

h 2 = xi 2 sin 2 F + ( -r-A- - xi cos F ) . 

\sin F / 


order to simplify the calculations it will be assumed 
that the distance from the reflection point to the 
target is large, so that the rays from the Fresnel 
zones may be considered parallel. With regard to 
the transmitter distance, however, no such approxi¬ 
mation will be made. 

hi = depth of the image antenna below the 
reflecting surface, in feet. 

F = angle of the lobe considered with reference 
to the tangent plane at the reflection point, 
in radians. 

m = number of the Fresnel zone. 

m = 0 for the center of the first zone. 

m = +1 for the far edge of the first zone. 

m = — 1 for the near edge of the first zone. 

m = +2 or —2 for the edge between the second 
and third zones. 

n = lobe number. For a given radar station n is 
related to the angle F by the equation 
n = (4/ii/X) sin F. 

X <= wavelength in feet. 

d n = distance from the transmitter to the near 
edge for the Fresnel zone and lobe considered, 
in feet. 

d f = distance from the transmitter to the far edge 
for the Fresnel zone and lobe considered, 
in feet. 

di = distance from the transmitter to the center 
of the first Fresnel zone for a particular lobe, 
in feet. 


iminating h from these equations and solving 

• Xi 

— m\ cosF + \/m 2 X 2 + 4mX/ii sin 4' . . 

Xi = - n • o ; T , -• 

2 sin 2 ^ 

>r the far point of the zone 


raX 


- + x 2 cos *) , 

\sin ^ / 


2 

iin 2 >F + + x 2 cos 'F ) . 

\sin \F / 


U~ = x 2 2 sin 

a similar process of elimination of l 2 and solving 
x 2 : 

w\ cos 'F + \/m 2 X 2 4- 4m\hi sin 'F 
* 2 = -2^h^-• (?6) 

the near point of the zone 

h i — m\ cos 'F -f \/m 2 X 2 + 4mX/ii sin 'F 
“ tarnF ~ 2 sin 2 >F 

ce sin 'F = nX/4/ii and F is small, cos F may be 
en as unity with the following error: 

up to 2 Yi less than 0.1 per cent, 

up to 10° less than 1.5 per cent, 

up to 15° less than 4.5 per cent, 

/I m N/m 2 + mn\ Shi 2 
dn ~ \2n + n 2 " n 2 ) X * 


n 




























THE CALCULATION OF VERTICAL COVERAGE 


161 


For the far point 

j _ ( 1 , m , \/m 2 + mn\ Shi 2 

df -\Zn + n* + J? ) ~X~ • 

These equations may be combined: 


d = 


( 1 m 's/m 2 4- mn\ 8/u 2 
\2n n 2 ~ n z /A 


(77) 


where the plus sign gives the far point and the minus 
sign gives the near point. The reflection point is 
obtained by using m = 0 and equation (77) reduces 
to: 


d l 


4 hi 

n\ 


(78) 


Thus to obtain the range of the near edge of the 
first Fresnel zone for the first lobe, substitute n — 1, 
m = 1 and use the minus sign in equation (77): 

d n = 0.688 ~ . (79) 

A 


The far edge of this zone is obtained by using the 
plus sign 

d, = 23.3 ^ . (80) 

A 


Equation (77) is in the form 

d = r Y ’ (81) 


where 

T - 8 (^ + 5 ± y^). 


(82) 


or 



(83) 


If di is taken as the distance of the shoreline, T i 
may be considered as a characteristic site or terrain 
factor at a particular azimuth and combined with 
the height and wavelength to obtain the range of 
any zone of any lobe. 

In order to read the relative intensity and phase 
lag of the reflected wave from the diffraction graphs, 
Figure 27 and Figure 28 respectively, it is necessary 
to have m expressed in terms of v. In Figure 19 the 
path difference is by definition of m 

A = m ^ . (84) 


Equation (23), with A = d — b, yields 



hence 

v 2 

m = \ . (85) 

It is also desirable to have an expression for v in 
terms of n and T. This is obtained by substituting 
v 2 /2 for m in equation (82) and solving 



The width of the zones, that is, along a chord at 
di parallel to the minor axis of the elliptical rings, 



may be obtained from Figure 60. Zone m is shown 
with a chord length b. The distance from the image 
antenna to the intersection of the chord and ring m 
is l + raA/2. From this may be written 

(<+¥)■-<•+©'■ to 

Neglecting m 2 A 2 /4 since it is small compared to the 
other terms, 

2 

V + m\l = l*+ (!) , 

b = \/ 4mA/ , 

l = = di = ^ ’ 

cos 'k n\ 

from equation (78), since ^ is small. 

Where earth curvature effects are appreciable the 




















162 


SITING AND COVERAGE OF GROUND RADARS 


effective height, from equation (59), should be used. 



To apply this method the distance of the shore¬ 
line, di, is substituted in equation (81), and the 
equation is solved for 7\, the terrain factor. This 
quantity is a constant for a particular azimuth and 
is substituted in equation (86) along with the values 
of n desired and solved for v. The values of m corre¬ 
sponding to these values of v are the numbers of the 
zones which intersect the shoreline for each value 
of n. These values of v are entered in Figures 27 and 
28 to obtain the intensity and phase lag relative to 
that which would be obtained if the rough land were 
replaced by the sea. 

Example 15. Shoreline Diffraction. A radar station 
is assumed to have the same height and frequency 
as in Example 11. The shoreline distance is 3 miles, 
and the intervening land is occupied by a large 
city, hi = 500 ft; / = 200 me; di = 15,840 ft. At 
this distance the effect of earth curvature is less than 
1 per cent and may be neglected. The greatest angle 
at which waves are reflected from the sea is given by 

iJgo X 57.3 = 1.81° . 

In equation (16) the maximum height of roughness 
for regular reflection is 


H = 


3,520 

200 X 1.81 


9.7 ft . 


The land is evidently a diffuse reflector. From 
equation (83) 


Ti 


d{k 

= WT 2 


15,840 X 4.92 
(500 - 4.5) 2 


Substituting in equation (86) for n = 2 


v 


4 


0.317 X 4 
8 


- 2 + 


2 

0.317 


2 . 11 , 


v 2 

m = ~ = 2.23 . 

That is, somewhat more than two zones are com¬ 
pletely formed on the sea. In order to determine 
which sign to use in reading Figure 27 it is only 
necessary to know whether the main reflection point 
di for this lobe falls on the land or the sea corre¬ 
sponding to shadow or illuminated regions. A more 
general procedure is to solve equation (63) using the 
shoreline distance for di : 


4 X (500 - 4.5) 2 
15,840 X 4.92 


12.6 . 


For all values of n less than 12.6, di will be on the 
sea and equation (84) applies to the near edge, and 
the minus sign is used in equation (82) corresponding 
to +v in Figure 27. For n greater than 12.6 the 
plus sign is used in equation (82) and — v in Figure 
27. Thus, for n = 2 and v = +2.11, is read in 
Figure 27 the relative intensity z — 0.980 and in 
Figure 28 the phase lag, £ = —0.103 radians. Other 
values are listed in Table 9. 

The width of the second zone may be computed 
from equation (88). The effective height for n = 2 
is obtained from Figures 50 and 51 and is 414 ft. 

b = 4 X 414 + = 1,656 ft . 


Table 9. Shoreline diffraction. (Example 15.) 


n 

V 

Sign 

z 

r 

n 

V 

Sign 

i z 

r 

0 

2.51 

+ 

1.036 

+0.080 

12 

0.14 

+ 

0.582 

-0.130 

1 

2.31 

+ 

1.083 

-0.015 

13 

0.089 

— 

0.459 

+0.2 

2 

2.11 

+ 

0.980 

-0.103 

14 

0.28 

— 

0.377 

+0.5 

3 

1.91 

+ 

0.884 

-0.038 

15 

0.49 

— 

0.308 

+0.9 

4 

1.71 

+ 

0.938 

+0.100 

16 

0.68 

— 

0.261 

+ 1.4 

5 

1.51 

+ 

1.082 

+0.120 

17 

0.87 

— 

0.223 

+ 1.9 

6 

1.32 

+ 

1.170 

+0.030 

18 

1.08 

— 

0.192 

+2.6 

7 

1.12 

+ 

1.156 

-0.085 

19 

1.27 

— 

0.170 

+3.3 

8 

0.92 

+ 

1.073 

-0.181 

20 

1.48 

— 

0.150 

+4.2 

9 

0.72 

+ 

0.953 

-0.255 

21 

1.67 

— 

0.135 

+5.2 

10 

0.52 

+ 

0.825 

-0.273 

22 

1.88 

— 

0.121 

+6.4 

11 

0.32 

+ 

0.696 

-0.224 

23 

2.07 

- 

0.111 

+7.6 


15.6.12 The Modified Antenna Pattern 

The vertical directivity of the antenna is modified 
by the local terrain. Unless the ground under the 
antenna is an extension of the reflection plane the 
modification of the free space directivity character¬ 
istics should be taken into consideration in the 
calculation of radar coverage. 

The vertical pattern of the antenna in the absence 
of a reflecting surface is referred to as the free space 
pattern, f A . This is usually given in the instruction 
manual for the set. If this pattern is not available 
or if the antenna has been modified, the vertical 
directivity may be computed by methods given in 
the next section. Local terrain effects are treated in 
some detail as they are in many cases a controlling 
factor. The resultant effect of the local terrain and 
free space pattern is called the modified antenna 
pattern, f(y). It does not include the effect of the 
main reflecting surface. 

















THE CALCULATION OF VERTICAL COVERAGE 


163 


15,613 Antenna Patterns 

To obtain f A , the relative amplitude of the radia¬ 
tion from the antenna, as a function of the vertical 
angle 7 it is only necessary to take into account the 
path differences of the elements of the array. The 
absolute field intensity and time phase will not be 
considered. In Figure 61 is shown an array of four 



horizontal half-wave dipoles spaced a half wavelength 
apart. The radiation from A in the direction 7 may 
be taken as proportional to cos c ct. The path differ¬ 
ence of radiation from B is A/ 2 -sin 7 . The corre¬ 
sponding phase difference is 

2x A . 

-— X o sin 7 = — 7 r sin 7 . 


For C and D the phase is — 2 x sin 7 and —37r sin 7 
respectively. The total field intensity pattern is 
f a. = cos c <ot + cos (cot — 7r sin 7) 

+ cos (cot — 2 x sin 7) + cos (cot — 3 x sin 7) , 

grouping 

[cos cot + cos (cot — 37r sin 7)] 

+ [cos (cot — 7r sin 7) + cos (cot — 2x sin 7)] . ( 89 ) 
From the identity 

cos A + cos B = 2 cos \ (A + B) cos J (A — B) 
equation ( 89 ) may be written 


f A = 2 cos 


(cot - y sin 7 ^ cos (~ sin 7 ^ 
+ 2 cos (cot — ^ sin 7 ^ cos (^ sin 7 ^ , 


= 2 cos (cot — ^ sin 7 ^ • 
j^cos^y sin 7 ^ + cos • (^ sin 7 ^ 


f A = 4 cos —— s i n yj cos s i n t) * 

cos (^ sin 7 ^ . 

Since only the rms value of this equation is signifi¬ 
cant, the terms containing cot may be dropped, and 
the result for the four-element array is 

f A = cos ( 7 r sin 7 ) cos (^ sin 7 ^ . (90) 

It is easily verified that this is a special case of the 
general expression for an N element array spaced at 
intervals of n\ and excited in phase (not derived here) 


/a 


sin (Nn 7 r sin 7 ) 
N sin (n x sin 7 ) 


(91) 


The effect of a reflecting screen may be computed 
by treating it as though it were A/4 from the dipole 
as in Figure 62. In practice the spacing may be 



more nearly A /8 but for 7 less than 30° the method 
given here is satisfactory and avoids a complicated 
analysis. The path difference QR is (A/2) cos 7 , and 
the phase difference is x cos 7 . Then 

f A = cos cot — cos (cot — x cos 7 ) . (92) 

From the relation 

cos A — cos B = —2 sin J (A + B) sin h (A — B) } 
it follows that equation (92) may be written in the 
form 


f A — — 2 sin (cot — ^ cos 7 ^ sin ^ cos 7 ^ . 

t 

Dealing only with the rms value, 

} A = sin (^ cos 7 ^ • (93) 


For small angles this factor is usually unimportant. 
Factors are given in Table 10 for some typical arrays 
with horizontal radiators in a vertical column and 
a reflector screen. 















164 SITING AND COVERAGE OF GROUND RADARS 


Table 10. 

Antenna pattern factors. 

Array with screen 

Vertical pattern f a 

Two radiators spaced ^ 

cos ^ sin 7 ^ sin cos 7^ 

Four radiators spaced ^ 

cos ^ sin 7^ cos (ir sin 7 ) sin cos 7 ^ 

Two sets of four radiators each 

cos ^ sin 7^ cos (ir sin 7 ) X 

(Vertical spacing between 
centers of sets is 3\.) 

cos (3 tt sin 7 ) sin cos 7^ 


Example 16. Vertical Pattern of an Antenna. Using 
the eight element array in Table 10 , the relative 
intensity at angle of 5° from the horizontal is com¬ 
puted as follows. 

f A = cos (90 sin 5°) cos (180 sin 5°) 
cos (540 sin 5°) sin (90 cos 5°), 

= cos 7°51' X cos 15°41' 

X cos 47°4' X sin 89°39', 

= 0.9906 X 0.9628 X 0.6809 X 0.9999, 
= 0.65. 

The main vertical lobe is plotted in Figure 63. The 
first null is at 9°36' and the half-power beam width 



Figure 63. Vertical pattern of a typical antenna. (Ex¬ 
ample 16.) 


is 4.53°. It will be noted that the effect of the 
reflector screen may be neglected for small angles. 

The pattern from a parabola is closely dependent 
on the feed system which controls the uniformity 
of illumination. To reduce side lobes it is common 
practice to taper the illumination toward the edge 
of the dish. This is accompanied by a broadening of 
the beam and a loss of gain. The half-power beam 
width for uniform illumination is 59 \/D degrees, 
where D is the diameter of the aperture. The first 


side lobe is then about 2 per cent of the maximum. 
A typical dish with a tapered feed would have a 
half-power band width of 68 . 8 \/D degrees. This 
reduces the first side lobe to 0.5 per cent. Some 
designs are further modified by deforming the dish, 
off-center feeds, etc., so that the patterns may not 
be easily computed. Such patterns are best obtained 
experimentally and are usually given in the manual 
for the equipment. 

15,614 Local Terrain Effects 

The vertical pattern of the antenna may be modi¬ 
fied by reflection from local flat areas or by diffraction 
over hills or other obstacles. To take these effects 
into account, factors are computed from the diffrac¬ 
tion equations which are used to modify the direct 
and reflected ray patterns. 

A detailed method of calculating /( 7 ) cannot be 
given because of the great variety of sites encoun¬ 
tered. However, the following discussion of the 
effects of particular terrain features will suggest 
methods of combining them to analyze a particular 
site. 

A large, flat land area will in general produce lobes 
and nulls at angles given by equation (57) with an 
envelope twice as large as the free space pattern. 
If the land area is not level, the lobe pattern will be 
tilted by the angle of the land. However, the problem 
is essentially a matter of diffraction since the land is 
of limited extent. Equation (16) should be used to 
determine whether the area is sufficiently flat to act 
as a regular reflector. 

If the land is flat from the antenna out to a 
distance d\ the relative intensity of the reflected ray 
is when di = hi X cot 7 . This assumes the land 
beyond di to be nonreflecting and that the distant 



























THE CALCULATION OF VERTICAL COVERAGE 


165 


boundary acts as a diffracting edge. As di increases 
further, the relative intensity increases to about 1.18 
and then decreases again and oscillates about unity 
in gradually decreasing swings. This is accompanied 
by a variation of phase. 

Several typical terrain problems will be solved in 
detail to illustrate the methods. 

Example 17. Limited Reflecting Area. A 200-mc 
radar, Figure 64, with an antenna as described in 


From Figure 27, using the plus sign for v 600 and the 
minus sign for ^ 3(0 oo, is obtained the relative intensity 

^6oo = 1 073; ^ 3,000 = 0.375. 

The reflection factor for n = 1 is given by 
2 = 1.073 - 0.375 = 0.698. 

From equation (57) 

1 X 4 92 

7 = Yx 5u = °- 0246 radian = L41 ° • 


h,*50 FEET += 200 MC 



v i — l - i 

O 4000 8000 l2pOO 

DISTANCE dj IN FEET 


Figure 64. Lobes from a limited reflecting area. 


Other values are given in Table 11. 


Table 11 . Limited reflecting area. (Example 17.) 


n 

7 

£>600 

£> 3,000 

2600 

23,000 

z 

fr 

/(7) 

0 

0 

+ 1.30 

+0.583 

1.177 

0.870 

0.307 

0.693 

0.693 

0.1 

0.14 

+ 1.26 

+0.498 

1.181 

0.810 

0.371 

0.658 

0.658 

0.4 

0.56 

+ 1.15 

+0.241 

1.164 

0.645 

0.519 

0.973 

0.973 

0.5 

0.70 

+ 1.11 

+0.155 

1.153 

0.592 

0.561 

1.147 

1.147 

0.6 

0.85 

+ 1.071 

+0.077 

1.142 

0.544 

0.598 

1.314 

1.314 

1.0 

1.41 

+0.918 

-0.279 

1.073 

0.375 

0.698 

1.700 

1.650 

1.5 

2.11 

+0.727 

-0.707 

0.960 

0.257 

0.703 

1.223 

1.137 

2.0 

2.82 

+0.535 

-1.136 

0.838 

0.186 

0.652 

0.349 

0.314 

3.0 

4.23 

+0.155 

-1.995 

0.592 

0.116 

0.476 

1.475 

1.090 

4.0 

5.64 

-0.237 

-2.853 

0.393 

0.082 

0.311 

0.689 

0.386 

5.0 

7.05 

-0.619 

-3.710 

0.277 

0.067 

0.210 

1.210 

0.436 


Example 16, is 50 ft above a smooth reflecting surface 
(a lake) which extends from 600 to 3,000 ft. From 0 
to 600 ft and from 3,000 ft on is rough land. The 
shore line diffraction method will be used to deter¬ 
mine the effect of the reflection from the limited 
area upon the antenna pattern f A . The vertical 
pattern is plotted from Figure 63 and shown dotted. 
To obtain the pattern for the reflected wave the 
shore at 600 ft is taken as a diffracting edge, and the 
relative intensity computed as a function of y as 
though the surface from 600 ft on were a perfect 
reflector. This is then repeated using the shore at 
3,000 ft. The difference between these two functions 
is then the effect of the area between 600 and 3,000 
ft. From equation (83) for n = 1 


600 X 4.92 
1 X (50)* 


1.18; T 3> ooo = 5.9 ; 



/1.18 


^600 — 

001 

X 
1—1 

1 

1 +08 


^ 3,000 — 0.279 . 


0.918 ; 


From equation (78) 

4 X (50) 2 
™ 600 600 X 4.92 


3.39 ; ft3,ooo 


The values of z multiplied by f A from Figure 63 
are plotted in Figure 65 as the reflected pattern. The 


DIRECT PATTERN - f A 


r-umtoi r« 


/ 


/ 


ANTENNA ^/^ / 


REFLECTING 
PLANE 


IMAGE 




REFLECTED PATTERN - zf A 


i_i_i-1-1-1 

0 0.2 0.4 0.6 0.8 1.0 

RELATIVE INTENSITY 

Figure 65. Components of the modified antenna for a 
limited reflecting area. 

resultant of the two vectors, f A and zf A , in terms of 
n is given by the cosine law: 

/r=V / l + z 2 — 2z cos ( mr ) . (94) 

Thus for n = 0.1 

f T = Vl + (0.371) 2 - 2 X 0.371 cos (O.lir) = 0.658 


= 0.678 . 




















166 


SITING AND COVERAGE OF GROUND RADARS 


The product of f T and f A is the modified antenna fac¬ 
tor f(y). This is plotted in Figure 64. With a larger 
reflecting surface, the length of lobes would approach 
twice the value of f A . Figures 64 and 65 were drawn 
for purposes of illustration and would not ordinarily 
be required. 

Example 18. Cliff Edge Diffraction. A 200-mc radar, 
Figure 66, with an antenna as described in Example 

h 1 =50 FEET 
CLIFF EDGE = 3000 FEET 
f= 200 MC 



Figure 66 . Cliff edge diffraction. (Example 18.) 


16, is 50 ft above a rough land surface, the top of a 
cliff whose edge is 3,000 ft away. 

The geometrical shadow line makes an angle with 
the horizontal of 

tan " (- dSo) = - °- 955 ° • 

At this angle, the relative intensity, z = 0.5. Other 
values of z may be read from Figure 27 after con¬ 
verting the angle of diffraction to v by means of 
equation (47). 

= -= o.6i e d °. 

4-92 

2 X 3,000 X 57 d 
At 0.377° in the shadow region v = —0.377 X 0.61 
= —0.23. From Figure 27, z is 0.4. This angle, 
referred to the horizontal at the antenna, is 

7 = * - 0.955 = —1.332°. 

Some other values are: 


7° 

z 

+3.535 

0.917 

+ 1.060 

1.18 

-0.955 

0.50 

-8.335 

0.05 


The modified antenna pattern f(y) is the product 
of 2 and f A and is plotted in Figure 66. This pattern 
gives the factors for both the direct and reflected 
waves for the sea lobes. 

Example 19. Land Reflection and Diffraction. This 
site is similar to that of Example 18 except that the 
cliff top is smooth. This is shown in Figure 67. 



Figure 67. Land reflection and diffraction. (Example 
19.) 


The smooth land causes land lobes to be formed 
as in Example 17 which furnish high angle coverage. 
The sea lobes are computed using the method of 
Example 18 for the direct and reflected rays. If the 
cliff top were tilted down, the land lobes would be 
tilted by the angle of the land. Speculation about 
complex sites yields many unusual patterns, but in 
practice the results are usually disappointing. Com¬ 
plex sites seldom have horizontal symmetry, and 
gaps in the coverage pattern may be expected. 
Attempts to reinforce the pattern in a particular 
direction by siting back from the cliff edge generally 
cause poor coverage at other angles. Best all-round 
CHL operation results from siting on cliff edges and 
exclusive use of the sea as a reflector. 

15.6.15 Earth Curvature Effect 

on Lobe Lengths 

The effect of earth curvature on lobe angles was 
described in Section 15.6.4. The angles to be used 
with the modified antenna pattern of the image 
antenna are affected by earth curvature, and there¬ 
fore the strength of the reflected wave is also affected. 
In Figure 68 is shown a radar antenna at height hi 
above the earth’s surface, with the center line of the 
antenna pattern parallel to GH, the horizontal at 

















THE CALCULATION OF VERTICAL COVERAGE 


167 



Figure 68. Earth curvature effect on direct and image patterns. Note: GH horizontal at the antenna; CE horizontal at 
the reflection point ft = 

ka 


the base of the antenna. Because of diffraction at a 
cliff edge the modified antenna pattern f(y) is unsym- 
metrical as in Example 18. The lines GH are parallel 
to the horizontal at the antenna. The line CE is 
horizontal at the reflection point and makes an angle 
ft with GH. The target is at an angle y with respect 
to GH. The incident and reflected rays make the 
angle y — ft with CE. It will be noted that the 
direct ray makes the angle y « 0 with the centerline 
of the antenna pattern, and the reflected ray makes 
the angle y — 2 ft. 


Coefficient of Reflection 

The coefficient of reflection of the reflecting surface 
is in general complex. That is, both the magnitude 
and phase of the reflected wave are affected. The 
reflection coefficient varies with the conductivity and 
dielectric constant of the reflector and with the 
frequency, polarization, and angle of incidence. 
Careful consideration should be given to the rough¬ 
ness of the surface, and a substantial reduction in 
the coefficient should be made when the height of 
roughness is comparable to that computed from 
equation (16). In general the reflection obtained 
with microwaves is of minor importance. 

The magnitude and phase angle of the reflection 


coefficient are plotted as functions of the angle of 
reflection, 'F in Figures 69 and 70. Curves are given 
for horizontal and vertical polarization and for the 
extreme conditions of sea water and dry soil. For 
dry soil the reflection coefficient is not sensitive to 
frequency changes, and the 100-mc curve may also 
be used for 3,000 me. 

For most purposes the reflection coefficient for 
horizontal polarization may be taken as unity, and 
the phase angle as 180°. The use of these values 
simplifies computations. 

The coefficients of reflection and phase angle for 
vertical polarization vary rapidly with frequency 
and angle of reflection for sea water and more 
gradually for dry land. The minimum point of the 
curves in Figure 69 is known as the pseudo-Brewster 
angle corresponding to a similar angle in optics. 

Cases not covered by Figures 69 and 70 may be 
computed from the following equations. 


Vertical Polarization: 


p exp (-70) 


€ c sin 'F — \Ze r — cos 2 'F 
e c sin 'F + e c — cos 2 \F ’ 


(95) 


Horizontal Polarization: 


p exp ( —j<f>) 


\/ e c — cos 2 'F — sin 'F 
V e c — cos 2 >F + sin 'F ’ 


(96) 






















0 DEGREES (LAG) P REFLECTION COEFFICIENT 


168 


SITING AND COVERAGE OF GROUND RADARS 


VT IN DEGREES 



Figure 69. Reflecting coefficient curves. 


}// IN DEGREES 



0 00)4 0.08 0J2 0.16 0.20 0.24 0.28 032 0.36 

}// ANGLE OF REFLECTION IN RADIANS 


Figure 70. Phase of reflection coefficient curves. Note: Solid curve represents seawater. Dotted curve represents dry soil. 
































































THE CALCULATION OF VERTICAL COVERAGE 


169 





Figure 71. Divergence factor graph. 


where 'F = the angle of reflection measured from the 
horizontal; 

e c = e r — j60crX; 

€ r = dielectric constant of the reflector rela¬ 
tive to air; 

a = conductivity of the reflector, mhos per 
meter; 

X = wavelength, in meters; 

</> = phase angle, lagging. 

Some typical ground constants are given in 
Table 12. 


Table 12. Terrain reflection characteristics. 


Type of terrain 

G 

( t , mhos 
per meter 

Fresh water 

81 

10- 3 

Sea water 

81 

1 

Rich soil 

20 

3 X 10“ 2 

Heavy clay 

13 

4 X 10~ 3 

Rocky soil 

14 

2 X 10" 3 

Sandy dry soil 

10 

2 X 10" 3 

City—industrial area 

5 

10" 3 



























































































170 


SITING AND COVERAGE OF GROUND RADARS 


15.6.17 


Divergence 


The reflected wave is scattered somewhat by being 
reflected from the spherical surface of the earth 
instead of a plane surface, and this reduction of field 
strength is taken into account by the divergence 
factor. This is dependent on geometrical considera¬ 
tions and may be expressed as follows (for y' < 3°): 


D 




1 + 


nX 


(97) 


2(5,280)* ( 7 ') 3 
where n is the lobe number, 

X is the wavelength, in feet, 
y' is the reflection angle, in radians, obtained 
from equation 60. 

A convenient chart for obtaining D is given in 
Figure 71. The parameters are y' in radians and nX, 
with X expressed in feet. 

As y' approaches zero, n also approaches zero, and 
the equation is indeterminate. At the point of tan- 
gency of the line of sight and the earth, D is 0.5773. 
At low angles the field is modified by diffraction 
around the curved earth. The lower limit of the angle 
y' for which the optical treatment is valid is usually 
given by 


> ^ 5 ®, > 0 0 “ 2 


(98) 


where k is % and X is in feet. 


For angles below this limit the theory for diffrac¬ 
tion of radio waves around the earth is required for 
a rigorous solution. However , in practice it is found 
that angles as low as the first maximum (n = 1) may 
be treated by the ray theory with little error. 

Applying equation (98) to Example 11 
y' > 0.00382 y/ 4.92 = 0.0065 radian. 

In Table 6 this corresponds to n = 2.25. However 
using n — 1 and y f — 0.0036 the divergence factor 
D is found from Figure 71 to be 0.58. For angles 
below y f = 0.0036 it is necessary to estimate D. 
Experience indicates that a fair minimum value to 
select for D is 0.5773. For angles much below the 
first maximum, the optical treatment gives values 
of field strength which are too low because it neglects 
diffraction. This may be compensated in part by 
using values of D between 0.5773 and 1.0. 


L = [/(y) ±f(y - 2d) zpD]d 0 (99) 

where L is the distance to the end of the lobes or 
the nulls, in miles. d 0 is the maximum range (in 
miles) at which a given response (usually the mini¬ 
mum detectable signal) would be obtained if the 
antenna were in free space. If the lobe diagram were 
plotted for some signal level above the minimum 
detectable, d 0 and L would be correspondingly 
smaller. 

Example 20. Lobes for a Medium Height Radar. A 
200 -mc radar using horizontal polarization has an 
antenna composed of two groups of dipoles spaced 
three wavelengths between centers, each group 
having four dipoles spaced X/2, as in Example 16. 
The antenna is 500 ft high and 3 miles inland as in 
Examples 11 and 15. It is desired to compute the 
vertical coverage pattern. 

From previous tests on this type of equipment it 
is known that the maximum range that would be 
obtained in free space d 0 is 80 miles. Since the 
polarization is horizontal, p will be taken as unity. 
Precision is not required for most of this kind of 
work, and it will suffice to compute values for equa¬ 
tion (99) at each integral value of n and to consider 
the values for odd n’s (with the plus sign) as the 
average of the lobe. The lobe shape will be taken 
as sinusoidal and the range at the nulls obtained by 
using even values of n and the minus sign; f(y) and 
/(y — 26) are obtained from Figure 63, by using 
values of y and y — 26 from Example 11 corres¬ 
ponding to integral values of n. The values of z are 
obtained from Example 15. The computations are 
shown in Table 13. Had cliff edge diffraction been 
involved f(y) and /( y — 26) would be read from 
curves as in Example 18 with marked effects on 
the pattern. 

The lobes are plotted in Figure 46 using equation 
(74) and the value of L for odd numbered n’s. For 
intermediate values of n the factors are: 


Fractional value of n sin (90° n) 

0.33 0.500 

0.50 0.707 

0.70 0.891 


15618 Lobe Lengths 

The contributions of the direct and reflected waves 
may now be added to obtain the length of the lobes. 


Using these three points above and below the lobe 
line and the maximum and minimum values from 
Table 13 the lobes may be plotted quickly as 
explained in Example 14. 






THE CALCULATION OF VERTICAL COVERAGE 


171 


Table 13. Lobes for a medium-height radar. (Example 20.) 


n 

/(7)/(7-2») z 

n /( 7-20) 

X P zD 

/(7) ± 

/(7 - 2 0) P zD 

L 

0 

0.999 

0.999 

1.036 

0.577 

-0.597 

0.402 

32.2 

1 

1.000 

0.998 

1.083 

0.580 

+0.627 

1.627 

130.2 

2 

0.999 

0.997 

0.980 

0.735 

-0.718 

0.281 

22.5 

3 

0.999 

0.994 

0.884 

0.823 

+0.723 

1.722 

137.8 

4 

0.997 

0.992 

0.938 

0.890 

-0.828 

0.169 

13.5 

5 

0.992 

0.989 

1.082 

0.912 

+0.976 

1.968 

157.4 

6 

0.989 

0.987 

1.170 

0.933 

-1.077 

0.088 

7.0 

7 

0.985 

0.981 

1.156 

0.942 

+ 1.068 

2.053 

164.3 

8 

0.980 

0.978 

1.073 

0.959 

-1.006 

0.026 

2.1 

9 

0.975 

0.972 

0.953 

0.963 

+0.892 

1.867 

149.4 

10 

0.970 

0.967 

0.825 

0.968 

-0.772 

0.198 

15.8 

11 

0.963 

0.961 

0.696 

0.973 

+0.651 

1.614 

129.1 

12 

0.958 

0.952 

0.582 

0.979 

-0.542 

0.416 

33.3 

13 

0.950 

0.947 

0.459 

0.981 

+0.426 

1.376 

110.0 

14 

0.941 

0.939 

0.377 

0.984 

-0.348 

0.593 

47.4 

15 

0.932 

0.929 

0.308 

0.987 

+0.282 

1.214 

97.2 

16 

0.923 

0.920 

0.261 

0.989 

-0.237 

0.686 

54.9 

17 

0.913 

0.910 

0.223 

0.991 

+0.201 

1.114 

89.1 

18 

0.903 

0.900 

0.192 

0.992 

-0.171 

0.732 

58.6 

19 

0.893 

0.890 

0.170 

0.992 

+0.150 

1.043 

83.5 

20 

0.881 

0.879 

0.150 

0.992 

-0.131 

0.750 

60.0 

21 

0.871 

0.869 

0.135 

0.992 

+0.116 

0.987 

79.0 

22 

0.857 

0.853 

0.121 

0.992 

-0.102 

0.755 

60.4 

23 

0.844 

0.841 

0.111 

0.992 

+0.093 

0.937 

75.0 


15.6.19 The Q enera j Lobe Formula 

The assumption of a sinusoidal lobe shape and the 
neglect of the phase of reflection and diffraction in 
the preceding section may in some cases lead to 
considerable error, especially when the direct and 
reflected waves are very different in strength. In 
general a more accurate method is required for sites 
over 1,000 ft in height, where vertical polarization 
is used or where it is desired to know the lobe shape 
in detail. The method given in this section provides 
a general solution of the coverage problem in the 
optical region (except along the bottom of the 
first lobe). 

The development of the lobe formula will be 
reviewed, and equation (99) will be given in a some¬ 
what different form. The expression for the electric 
vector due to the direct wave is 

E d = ~ f(y) exp (- j2 t r^) . ( 100 ) 

For the reflected wave 


E r = electric field intensity at the target 
due to the reflected wave, microvolts 
per meter; 

E\ = electric field intensity at 1 mile in 
the equatorial plane of the antenna, 
microvolts per meter; 

/( 7 ) = modified antenna factor for the direct 
wave (Section 15.6.12); 

f(y — 20 ) = modified antenna factor for the 
reflected wave (Section 15.6.15); 

R = a complex factor for the reflected 
wave given by 

R = D P z {exp[—_/(<#> + £)]} ; (102) 

where D = divergence factor (Section 

15.6.17); 

p exp (— 7 $) = complex reflection factor (Section 
15.6.16); 

z exp (— j£) = complex diffraction factor (Section 
15.6.11). 


The net field at the target is 

E t = Ed + E r , 



/( 7 ) + /(7 - 20 ) 


D p z {exp [ — j(4> + f + 5)]) , 


(103) 


considering only the absolute value of E T and taking 
r = Td = d except where the path difference is 
involved. The path difference phase shift is 


2tt , \ 

5 = y (r - r d ) . 


(104) 


Equation (103) may for convenience be written 

I e t \ = !jA- (ios) 


The target is assumed to have a complicated form 
and to be changing its aspect constantly. The 
reflected energy is considered to be of random phase 
and magnitude. The magnitude of the reradiated 
field (microvolts per meter at a distance of 1 mile 
from the target) is found by using a coefficient of 
reradiation, p T , which varies with the target and 
aspect. 

The received field intensity is by the reciprocity 
theorem: 


E r = ^rf(y ~ 20) R exp j2 t 0 , ( 101 ) 

where Ed = electric field intensity at the target 
due to the direct wave, microvolts 
per meter; 


\E\ = pr 1 ^ A . 

Substituting from equation (105) 

1*1 


(106) 












172 


SITING AND COVERAGE OF GROUND RADARS 


For a particular coverage contour, such as the 
threshold of detection, usually taken as a signal-to- 
noise ratio of unity, a minimum received field inten¬ 
sity | E n | may be assumed. This is related to receiver 
noise voltages, antenna gain, and other factors of 
design. Using | E N | for | E | and solving for d 


d 


-4 


Pt I E\ | 


I E 2 


A = d 0 A . 


(107) 


Because of the way in which Ei and p T are defined, 
do, the maximum free space range, has the dimen¬ 
sions of length (in miles). It depends on the design 
of the transmitter and receiver and on the target. 
A may be considered a coverage factor which depends 
on 7 and terrain effects. 

Because of the implicit character of the parameters 
of A in equation (103), a general solution of A as a 
function of 7 is not feasible. However, examination 
of typical problems discloses that the range of varia¬ 
tion of some of the factors is limited, and a method 
of successive approximations may be readily applied. 


In most cases 0 and will vary slowly (about as 
fast) compared to 8 below 2 ° or 3°. At higher angles 
the rate of change may be faster, but contribution 
of the reflected wave at these angles is likely to be 
unimportant. 

The method described here consists in computing 
the lobe angles, diffraction, and divergence as though 
the only phase shift involved was that due to path 
difference as in Sections 15.6.4, 15.6.11 and 15.6.17. 
The phase shifts from the apparent lobe angles thus 
computed are then determined. The diffraction phase 
shift is and the reflection phase shift is 

0' = 0 - 180°, (108) 
where 0 is obtained from Figure 70. If horizontal 
polarization is used 0 may be taken as 180°, and 
0' is then zero. With curves of the phase shift 
0 ' + T and the product /(7 — 2 6)Dpz plotted 
against 7 the apparent lobe angles and lengths 
computed above may be corrected to obtain the 
actual values. The details of this method will be 
given in the example below. 



#IN RADIANS 

Figure 72. Relative magnitude and phase of the reflected ray. 








































THE CALCULATION OF VERTICAL COVERAGE 


173 


Example 21 . The General Lobe Formula. An inter¬ 
rogator equipment is used with the radar of Example 
20. It operates on 160 me; the height of the antenna 
above the sea is 500 ft; and the distance to the shore 
is 15,840 ft. The intervening land is too rough for 
coherent reflection. The antenna consists of two 
vertical radiating elements and parasitic reflectors. 
The radiators are approximately a half wavelength 
long and spaced a half wavelength apart. The maxi¬ 
mum distance art which reliable interrogation may 
be obtained in the absence of a reflecting surface 
has been found to be 110 miles for this particular 
equipment. It is desired to construct for this site 
the vertical coverage diagram of the interrogator 
system. 

The vertical pattern of a vertical half-wave dipole 



Since this factor is over 0.98 for angles up to 10 
degrees, f(y) and f(y — 26) will be taken as unity. 
The lobe angles are then computed neglecting 0 and 
f, as in Example 11 . Diffraction and divergence are 
computed as in Example 15 and Section 15.6.17. The 
results of these calculations are listed in Table 14. 

The values of p and </> depend on y ' and are read 
from Figures 69 and 70. Using equation (108), <t> f 
is obtained and added to f. The sum 4> f + f is the 
net phase shift of the reflected wave from the values 
used in computing the lobe angles and is plotted 
against y in Figure 72. For purposes of comparison 
8 has also been plotted, but this curve is not required 
otherwise. The product Dpz is the relative strength 
of the reflected ray and is plotted in Figure 72. 

The points on the coverage diagram are obtained 
in polar form from equation (107). 

d = 110a/ 1 + ( L>pz) 2 — 2 Dpz cos (</>' + f + 6 ) . 

The vector representing the reflected wave is shifted 
in the lagging direction by 0 ' + £ degrees when this 
sum is positive, and in the leading direction when 
the sum is negative. The effect of this phase shift 
on the point on the lobe being considered may be 
determined by inspection of Figure 72. 

Thus, to determine the first maximum point the 
following procedure may be used. At n = 1 the 
angle y is 0.0011 radian and 0 ' + f is —14.8 degrees. 
This means that for the cosine term to be —1 the 
path difference must be increased until 8 is 194.8 
degrees. The angle yd at which this value of 5 occurs 


is found by interpolating between 0.00110 and 
0.00492 since 8 changes from 180° to 360° in this 
interval. This angle is then 0.00141 radian. Had the 
angle 0 ' + f changed appreciably from 0.00110 to 
0.00141 the interpolation would be repeated using 
the new value of 0 ' + In most cases the new 
value of 0 ' + f may be estimated from the curve, 
and the first approximation will be close enough. 


Table 14. The general lobe formula. (Example 21.) 


n 

Y 

radians 

7 

radians 

z 

r 

D 

7 a 

radians 

d 

0 

0 

-.00600 

1.061 

- 2.86 

1.000 

-.00589 

0 

1 

.00421 

+.00110 

0.920 

- 5.27 

0.640 +.00141 

165.0 

2 

.00712 

.00492 

0.897 

+ 3.04 

0.792 

.00527 

48.5 

3 

.01000 

.00835 

1.039 

+ 7.56 

0.862 

.00858 

180.5 

4 

.01295 

.01163 

1.158 

+ 2.75 

0.908 

.01206 

36.3 

5 

.01595 

.01485 

1.158 

- 5.04 

0.938 

.01557 

178.5 

6 

.01897 

.01802 

1.067 

- 10.88 

0.955 

.01894 

52.7 

7 

.02200 

.02119 

0.930 

- 15.00 

0.963 

.02225 

155.6 

8 

.02500 

.02428 

0.779 

- 15.00 

0.969 

.02544 

66.5 

9 

.02810 

.02744 

0.648 

- 11.00 

0.973 

.02860 

137.0 

10 

.03110 

.03051 

0.500 

0.00 

0.982 

.03161 

89.1 

11 

.03420 

.03365 

0.408 

+ 17.18 

0.984 

.03453 

126.4 

12 

.03720 

.03669 

0.332 

+ 43.0 

0.987 

.03731 

96.6 

13 

.04050 

.04005 

0.267 

+ 74.4 

0.991 

.04024 

120.6 

14 

.04330 

.04288 

0.222 

+ 108.9 

0.991 

.04253 

100.7 

15 

.04640 

.04600 

0.190 

+ 154.6 

0.992 

.04493 

117.7 

16 

.04950 

.04912 

0.165 

+206.2 

0.993 

.04894 

103.0 

17 

.05250 

.05216 

0.143 

+263.3 

0.993 

.05010 

116.5 

18 

.05560 

.05528 

0.129 

+326.2 

0.994 

.05264 

104.0 

19 

.05870 

.05840 

0.114 

+412.3 

0.995 

.05479 

115.6 

20 

.06170 

.06142 

0.104 

+492.6 

0.997 

.05694 

104.5 

21 

.06480 

.06454 

0.094 

+590.0 

0.998 

.05909 

114.6 

22 

.06780 

.06755 

0.089 

+687.0 

0.998 

.06127 

105.6 

23 

.07090 

.07067 

0.081 

+813.0 

0.998 

.06436 

114.2 


At 0.00141 radian Dpz is 0.501. Substituting this 
value: 

d = 110-n/i + (0.501) 2 - 2 X 0.501 X (-1) 

= 165.0 miles , 

which is laid off on the coverage diagram at an angle 
of 0.00141 radian. As many other points as required 
to sketch the diagram may be computed in a similar 
fashion. For an intermediate point it is convenient 
to use the net angle equal to 90° since the equation 
then reduces to 

d = 110-s/l + • 

The angles of the lobes have been listed in Table 14 
under yd and the lobe lengths under d. 

The vertical coverage diagram is shown in Figure 
73. The lobe maxima and minima and the 90-degree 
points have been sufficient for sketching the lobes 
except on the first lobe where a few additional points 
have been computed. When the net angle is 60 
degrees, the field strength at the bottom of the first 












174 


SITING AND COVERAGE OF GROUND RADARS 



lobe is equal to the free space field. At ranges shorter 
than this the reflected wave opposes the direct wave. 
Directly under the antenna the contour passes near 
the surface so that the waves are very nearly in 
opposition. Because of the variation in Dpz with 7 
the maxima will not occur exactly when the cosine 
is unity, but this effect is generally negligible. 

157 CALIBRATION AND TESTING 
15-71 Introduction 

It should not be inferred from Section 15.6 that a 
reliable coverage diagram can be obtained by calcu¬ 
lation alone. Under field conditions it is necessary 
to make test flights and other checks before equip¬ 
ment can be depended upon to meet a calculated 
performance. On the other hand it is seldom possible 
or desirable to obtain a satisfactory coverage diagram 
from tests alone. Best results are attained when tests 
and analysis supplement each other. 

Test flights are arduous, expensive in personnel 
and materials, and time consuming. In most theaters 
a number of agencies become involved, and careful 
planning and organization are required to achieve a 
useful result. For these reasons the amount of test 
flying should be held to a minimum by intensive 
analysis and equipment tests before and after the 
test flights. “Calibration and testing” might well be 


a book in itself, but only a very brief discussion will 
be given here for the sake of completeness. 

157 2 Equipment Tests 

It is difficult to overemphasize the importance of 
proper equipment maintenance. An unfortunate ten¬ 
dency of inexperienced personnel is to maintain on an 
emergency basis, rather than as a matter of system¬ 
atic routine. In most cases the need is for a careful 
check of all elements and restoration to as-good-as-new 
condition, rather than a brilliant intuitive process 
known as “trouble shooting.” One survey of a large 
number of systems disclosed an average reduction 
from optimum performance of 13.5 db. This corre¬ 
sponds to a maximum range of 50 per cent of normal. 
Careful tests have shown the use of “standard tar¬ 
gets” to be very misleading in many cases. Large 
changes in the maximum ranges of small targets 
were found without appreciable changes in the 
strength of the permanent echoes used for checking 
purposes. 

Full use of test instruments available should be 
made in checking the equipment. Orientation should 
be completed and the accuracy of range and azimuth 
indicators checked. Tuning and modifications should 
be done before the test flights are made, unless the 
tests indicate poor performance. A great handicap 





















































CALIBRATION AND TESTING 


175 


A SCOPE SENSITIVITY-LOW 



in tire work e the lack of absolute measures of power 
output, bat mock may be done with echo boxes and 
fieW intentrity meters. Reference is made to service 
publications and instruction manuals for further 

detafe 

Signal Measurements 

Several methods are used for recording si g n a l 
strengths- and these determine the type of receiver 
calibration required. Estimation of signal-to-noise 
ratios by means of scales on the face of the scope 
requires some means of specifying the gain setting. 
The means reed, such as height of noise, position of 
gam dnL and so forth, should be calibrated with a 
signal generator so that there is an assurance of 
adequate sensitivity and a way of checking the 
measurements. The saturation line on the scope is 
assigned a height of 10^. and the signal and noise 
heights are read in proportion- Ratios in excess of 
10 are usually read as 10-K This method requires 
considerable drill on the operator's part and is 
lizir: *1 - - - In Jlt - ~ -bi” i :-i~ n 

ewrve on a typical “square law™ receiver. In the circle 
i? represented a sgnal on an A scope which would 
commonly be read as a signal-to-noise [S N] ratio 
of S- Actually the ratio of receiver inputs correspond¬ 
ing to the signal and noise heights is $.5 3.25 or 2.6. 

A considerable improvement over the above 
method may be obtained as follows. An index fine 
b drawn on the face of the A scope about an inch 


from the baseline. To measure a signal it is brought 
to the index fine by adjustment of the gain control, 
and the gain control voltage is recorded. The gain 
voltage required to bring the noise to the index fine 
is also noted occasionally during the test. A calibra¬ 
tion curve is made using a pip signal generator or a 
modulated signal generator connected to the receiver 
input. The gain voltage required to bring the signal 
to the index line is measured for various inputs. 
Gain voltage readings on the test target and noise 
are converted by means of the curve to equivalent 
input voltages. Test data may be conveniently 
plotted as decibels above noise after this conversion. 
It should be noted that the calibration depends upon 
the type and percentage of modulation. 

A third method involves calibration of the gain 
control dial by comparison of permanent echoes. 
Three fines are drawn on the scope face such as J4, 
1. and 1J4 in. from the baseline. The position of the 
gain dial with the noise at in. is marked 0 db. A 
permanent echo is selected which comes to the 1-in. 
fine at this setting. The gain dial is then turned to 
bring this echo to the 3^-in- mar k, and this position 
of the dial is marked 6 db. Another echo is then 
selected which is 1 in. high, and it is brought down 
to J4 in. by further adjustment of the gain dial. This 
position is marked 12 db. In this manner the gain 
dial ma y be calibrated over the full range of adjust¬ 
ment. It may be necessary to change the series 
resistor on the gam potentiometer to spread the 






























L76 


SITING AND COVERAGE OF GROUND RADARS 


working part of the scale over a sufficiently wide 
angle. A common difficulty with this method is lack 
of suitable permanent echoes (Section 15.5.3). 

A fourth method is suitable for microwave gear 
where search is conducted with a PPI scope. As the 
beam sweeps past the target a hit or miss is recorded. 
If desired, additional note may be made such as miss, 
very weak, weak, or hit. In analyzing the data the 
percentage of hits in an arbitrary period of 30 sec is 
plotted against range, counting very weak signals 
or stronger as a hit, as in Figure 75. The data may be 



for various contingencies. Changes from prearranged 
plans should be held to a minimum. Close liaison 
should be maintained with the flight section and 
every effort made to avoid hazardous flying. Where 
feasible, flights over sea should pass near landmarks, 
etc., to check navigation. Other radars and agencies 
should be employed to assist the test plane in holding 
its course. The permanent echoes should be noted 
during the test and compared with average condi¬ 
tions so that an estimate of nonstandard propagation 
may be made. Similar checks should be made at other 
nearby radars. 

157 5 Analysis of Test Data 

Test data should be accompanied by a complete 
description of the conditions of the test. Data should 
be analyzed promptly, and every effort should be 
made to extract the full amount of useful information. 

In Figure 76 is shown a signal-to-noise graph for 


Figure 75. Test flight data for PPI scope. 

scattered, but it is not difficult to decide the range 
at which the percentage of hits is 50 per cent. This is 
taken as the maximum range. At lower altitudes 
a lobe structure may be detected, indicating ground 
reflection. 

15 7 4 Conduct of Test Flights 

The test planes should have two or more engines. 
Slow-speed, high-ceiling, long-range planes are most 
desirable. They should be equipped with navigational 
aids such as radio compass, DF system, and loran, 
and full complement of communication sets, trans¬ 
ponders, and altimeters. For positive identification 
in regions of high traffic density, a distinctive IFF 
(identification friend or foe) response is essential. 
Mark II transponders may be readily modified in 
the YHF band to give a double pulse by shifting 
the condenser rotors. 

Tests are conducted by flying out from the station 
and returning at a specified altitude to a range 
estimated to be about 10 per cent beyond the maxi¬ 
mum of the lobes. Suitable altitudes are from 5,000 
to 20,000 ft. Little is learned from tests below 1,000 
ft since nonstandard propagation effects are most 
pronounced in this region. 

Data should be taken by specially trained opera¬ 
tors as considerable judgment is required. Flights 
should be carefully planned and full provision made 



a station similar to Example 20. The noise is set at 
a relative height of 1, and the signals are read in 
proportion as the plane comes in. The weak signals 
at medium ranges are due to shore line diffraction. 
The peaks correspond to lobe maxima and ranges at 
S/N = 1 to the locations of the lobe contour at 
12,000 ft. The receiver in this case is of the “linear” 
type, and the lobe maxima may be obtained by 
extrapolation. Along a line of constant path difference 
such as the maxima of the lobes the signal-to-noise 
ratio varies as the inverse square of distance. Thus 
the fourth lobe has a peak S/N ratio of 6 at 68.5 
miles, and the lobe length isL = 68.5 V 6 = 167.5 
miles. 

In practice the length computed in this manner 
would be compared to those obtained from tests at 
other altitudes. Notes made during the test and other 
factors would be considered and the data weighted 
accordingly. For example, at 90 miles the S/N ratio 

























CALIBRATION AND TESTING 


177 



\ 



is 2 and the percentage error is probably greater than 
on the reading at 68.5 miles. The location of points 
on the lobe cannot be read with accuracy from Figure 
76 at S/N = 1 since this is threshold data which 
may be in considerable error. 

To determine the maximum free space range F, 
the lengths of the lobes obtained from the test data 
may be listed along with the site factors from equa¬ 
tion (99) or equation (107). A value of F is then 
selected which will most nearly fit the test data. 
Variations in performance of the equipment affects 
the lobe lengths in proportion. Variations from the 
standard atmosphere assumed will shift the position 
of the lobes, particularly at low altitudes. 

Where better accuracy is desired or the receiver is 
nonlinear, the calibrated receiver method is required. 
Such data are recorded as gain voltage, range, and 
time. For each gain voltage, the equivalent receiver 
input voltage is read from a calibration curve such 
as Figure 74. The equivalent value of the noise 
voltage of this set is 30 ;uv. Dividing the equivalent 
receiver signal voltages by 30 gives the S/N ratio 
which is plotted against range in Figure 77. The 
lobes are identified by reference to a lobe angle 


diagram. The extrapolated lobe lengths may be listed 
as follows: 

Height, feet Length of lobes, miles 

12 3 4 

20,000 ... 243 196 235 

10,000 159 212 169 162 

5,000 156 216 163 158 

The 20,000-ft data were taken last and indicate the 
effect of certain equipment adjustments. The ability 
to maintain this performance is one of the questions 
to be considered in arriving at a weighted average 
value of lobe lengths. Comparison of these lobe 
lengths with the computed lobe factors will indicate 
a fair value to be used for the free space maximum 
range. 

Until suitable instruments are provided for 
measuring set performance the conduct of successful 
tests will continue to be a challenge to the ingenuity 
and diligence of field personnel. However, with a 
careful analysis of the propagation characteristics of 
a given site and radar equipment and a well-conducted 
test with inadequate instrumentation minimized by 
determined improvisation, it is still practical to 
obtain a reliable solution to the coverage problem. 


















































Chapter 16 

VARIATIONS IN RADAR COVERAGE 


V ariations in coyerage of radio and radar 
equipment are caused by atmospheric factors 
which influence propagation of very short radio 
waves. 

The rapid and accurate evaluation of radar signals 
is dependent to a great extent upon our knowledge 
and understanding of the effects produced by the 
variable conditions of the lower atmosphere. 

Evaluation of radar signals influenced by weather 
introduces problems of identification, actual range 
determination with second or third sweeps, and radar 
coverage characteristics, each having a direct bearing 
on the tactical situation. 

Enemy ships far beyond the horizon have been 
located by radar and sunk by radar-controlled gun¬ 
fire. United States warships in the Pacific, in several 
instances, have picked up targets by radar at ranges 
four to five times those obtained under standard 
conditions. 

Army coastal radars have tracked convoys on 
some occasions to 20 or 30 miles beyond normal 
radar ranges. The same radars, a few hours later, 
may have failed entirely to pick up targets clearly 
visible to the eye. 

Allied forces are employing radar and VHF (very 
high frequency) equipment with steadily increasing 
effectiveness. But we are forced to revise and improve 
our early conceptions of the capabilities and limita¬ 
tions of these useful instruments of World War II. 
Serious errors and false evaluation of radar presenta¬ 
tion may result if we do not take into consideration 
the effects of weather and atmosphere on radar 
ranges and VHF coverage. 

Complete reports of the variability of radar cover¬ 
age show that certain weather and atmospheric 
conditions prevailing along the transmission path 
may greatly modify the normal range characteristics 
of radar and VHF radio. The operator, at certain 
times, can “see” targets or hear messages far beyond 
the horizon, sometimes at unbelievable distances. At 

^his document was published June 1, 1944 and distributed 
widely to Service personnel under the above title, and under 
short title JANP 101, by authority of the Joint Communica¬ 
tions Board. Originally prepared by the Columbia University 
Wave Propagation Group, it was amended and improved by 
representatives of both Services in an effort to prepare a brief, 
qualitative but authoritative statement of the then known 
facts concerning the factors contributing to nonstandard 
propagation. 


other times he is unable to contact, by radar or 
VHF, aircraft or surface craft well within the normal 
range limit. 

These effects of a nonstandard atmosphere might 
leave doubt in our minds as to the effectiveness of 
radar and the usefulness of VHF radio. But we should 
adopt the reverse view. We can, by understanding 
and allowing for these phenomena, make a useful 
instrument more effective—the weather will work for, 
instead of against, radar and microwave equipment. 

Unusual ranges are caused by bending or refraction 
of the radio waves by the atmosphere. A most import¬ 
ant special case of refraction is the concentration of 
the wave energy in ducts within the atmosphere. 
This bending and duct formation is a direct result of 
the meteorological factors involved—factors of 
weather and atmosphere—peculiar, in many cases, 
to the locality and the season. Such factors are dis¬ 
cussed later. 

161 BENDING 

The VHF or radar operator usually assumes that 
short waves and microwaves, at frequencies above 
about 30 me, travel along the line of sight from the 
transmitter to the receiver and, in the case of radar, 
to and from the target. Experience has shown that 
this assumption, nearly true in many instances, may 
lead to serious errors or false evaluation if applied 
to radar operation and microwave communication. 

Radio waves are bent from a straight line path as 
a result of refraction by the lower atmosphere. This 
bending, or refraction, is generally recognized as a 
property of light. It is equally a property of radio 
waves. The underlying principles are exactly the 
same in both cases. 

The quantity that determines refraction is called 
the index of refraction. Refraction occurs whenever 
there is a change of index of refraction, as at the 
boundary of two substances. In the interior of a 
material of constant refractive index, the rays travel 
in a straight line. The change in angle at the bound¬ 
ary is the larger, the greater the difference in refrac¬ 
tive index from one material to the next. 

Radio waves are refracted or bent in the atmosphere 
because the index of refraction of the atmosphere 
changes with height. The properties of the atmos¬ 
phere which determine the refractive index and which 


178 



BENDING 


179 



Figure 1 . Actual pattern showing radar coverage for standard propagation. 



Figure 2. Modified presentation of the information shown in Figure 1. 


change with height are temperature, pressure, and 
moisture content. These changes from one level to 
another are very small compared with that from 
water to air, and the resulting refraction itself is 
small. Nevertheless this refraction is of great import¬ 
ance in radar operations and radio communications 
above 30 me. 

If the atmosphere were composed of a number of 
successive layers each having a different index of 
refraction, a wave passing across the successive boun¬ 
daries of the layers would be abruptly deflected at 
each surface. The atmosphere does not consist of such 
distinct layers. Instead, the change in its physical 
properties and its index of refraction is gradual, 
continuous. There is, then, no sudden change in 
direction of the waves; the change in direction 
becomes gradual and continuous. In other words, a 
bending of the waves occurs as they pass through 
the atmosphere. Radio waves passing through the 
lower atmosphere are usually bent downwards. 

As can be seen from the illustration of the actual 
pattern (Figure 1), the bending of the waves, or rays, 
by the atmosphere permits one to see farther than 


he would otherwise. In the figure the vertical dimen¬ 
sions have been strongly exaggerated so that the 
earth’s curvature becomes clearly visible. Under 
average weather conditions the horizon distance is 
increased by about 15 per cent, but at an elevation 
near the first lobe the increase in range is much less 
than this amount. This is the case of standard 
refraction, or standard propagation. 

It is rather inconvenient to draw curved rays in 
radar coverage and calibration diagrams. This can 
be avoided by assuming that the earth’s radius is 
% the actual radius. Then in the diagrams the rays 
appear as straight lines when the propagation is of 
the standard type. This method often is adopted in 
radar calibration practice, with coverage diagrams 
drawn or printed to the % value of the earth’s radius 
(see Figure 2). This corrects for the effect of normal 
bending in the atmosphere. The radar operator 
merely plots the position of his target on such a 
diagram and assumes that the radiation travels along 
a straight line between the radar and the target. In 
this way he takes into account the effects of standard 
refraction while doing his work. 

















180 


VARIATIONS IN RADAR COVERAGE 



Figure 3. Radar lobe pattern in nonstandard atmos¬ 
phere. A duct has been formed on the surface of the 
ocean and a ship is detected. Lobe No. 1 is bent down¬ 
ward more than normal, but the other lobes remain sub¬ 
stantially unchanged by the duct. 

Wave propagation deviating from standard occurs 
under special weather conditions. The most import¬ 
ant type is called “guided propagation/’ “trapping/’ 
or “superrefraction”—formerly referred to as 
anomalous propagation. The main feature of this 
type of propagation is an excessive bending of the 
rays due to refraction. This bending occurs prin¬ 
cipally in the lower layers of the atmosphere and 
mainly in the lowest few hundred feet. In certain 
regions, notably in warmer climates, excessive bend¬ 
ing is observed as high as 5,000 ft. The amount of 
bending in regions above this height is almost always 
that of the standard atmosphere. 

As a consequence of the excessive bending in the 
lower layers the coverage pattern of a radar set is 
deformed, as illustrated in Figure 3. The fact that 
atmospheric influences are effective only in the lower 
layers does not imply that the echo strength from a 
target will be affected only as it lies in these layers, 
though the effects will be strongest there. It merely 
means that excessive bending is suffered by the rays 
only while passing through the lower layers. How¬ 
ever, the deformation of the coverage pattern itself 
will in general extend to a greater height. 

Two factors are operative in producing a rapid 
change of refractive index with height: variation of 
moisture with height and variation of temperature 
with height. Excessive refraction occurs when there 
is a rapid decrease of moisture with height (“moisture 
lapse”) and, to a lesser degree, when there is a rapid 
increase of temperature with height (“temperature 
inversion”). The most pronounced cases of excessive 
refraction occur when both these conditions prevail 
at the same time. These conditions will be discussed 
later from the meteorological viewpoint. 


Since the atmosphere is a very tenuous substance, 
the amount of refraction, that is, the amount of 
angular deflection of the rays, is very small and in 
no case exceeds a fraction of a degree. How then can 
these small effects influence radar operations? The 
answer is that they do not influence operations unless 
the angle between the ray itself and the horizontal 
is very small. If radar is used for fire control, search¬ 
light control, or fighter intercept control, the targets 
are usually at medium or short ranges, and the angle 
between the line of sight and the horizontal is usually 
larger than one to two degrees. Refraction has 
practically no effect on such an application of radar. 

However, the same equipment may be used for 
long-range search and then the story is different. 
With early warning radar the target may be an 
airplane 50 or 100 miles away, and it may fly at an 
elevation of only a few thousand feet. In this case 
the angle of elevation of the target above the hori¬ 
zontal, as seen from the radar, is only a fraction of 
a degree. This applies still more to seaborne targets. 
The atmospheric effects then become operationally 
important. It should always be kept in mind that 
only low-angle search is affected by meteorological 
conditions. 

As a rule, the operational characteristics of a radar 
for angles of elevation of the target exceeding 1 
degree may be calculated on the assumption of a 
standard atmosphere, with confidence that all non¬ 
standard meteorological effects are negligible. 



Figure 4. Wave paths illustrated as rays in ground- 
based duct. 


162 GUIDED PROPAGATION 

It is obvious that excessive bending of the rays in 
the lower layers of the atmosphere must distort 
radar coverage patterns. One case of special import¬ 
ance is illustrated in Figure 4. Four rays, out of 











GUIDED PROPAGATION 


181 


many, are shown which leave the transmitter at 
different angles with the horizontal. 

Ray 1 is bent so much that after some distance it 
returns to the ground; there it is reflected and then 
the same course is repeated again. In this way the 
ray may be reflected a number of times in succession, 
remaining always in the lowest layer. This super¬ 
refraction “traps” the rays in a “duct” and results 
in guided propagation of the radar waves. Trapping 
does not occur under standard atmospheric condi¬ 
tions. A ray, under standard conditions, may be re¬ 
flected by the earth's surface only once before it 
escapes into space. 

Ray 2 is also bent in the lowest layer but not 
enough to keep it from escaping into the upper 
atmosphere whence it does not return to earth. 

Ray 8 is similar to 2 except that it undergoes one 
reflection by the ground before it escapes into the 
upper atmosphere. 

Ray 4 separates the two types of rays illustrated 
by rays 1 and 2. This ray becomes horizontal when 
it reaches the top of the trapping layer or duct and 
from there on travels along at the same height. All 
rays are divided into two groups: those that leave 
the transmitter at an angle with the horizontal less 
than the critical angle and are trapped, and those 
that leave the transmitter at a larger angle and 
proceed into the upper atmosphere. 



Figure 5. Rays in an elevated duct. In this, another 
common form of duct, the amount of bending may be 
approximately normal both below and above the duct. 
The rays oscillate between the upper and lower bound¬ 
aries; maximum ranges in or near the duct may be even 
greater than with a ground-based duct. 

The critical angle is aways small, practically never 
larger than degree. Its magnitude may be taken 
as a measure of the intensity of guided propagation, 
that is, of the amount of radiant energy trapped 
within the duct. Rays that leave the transmitter at 
a somewhat larger angle up to about twice the critical 


angle are sufficiently deflected while passing through 
the lowest layers to distort that part of the radar 
coverage pattern lying just above the duct. Rays 
leaving the transmitter at a still larger angle are not 
appreciably affected. 

The ground-based duct or trapping layer guides 
the wave along the earth's surface in much the same 
way that hollow metal tubes guide microwaves. 
Within the duct there is less decrease of signal 
strength with distance than there is above the duct. 
Radar ranges on surface craft and low-flying aircraft 
located within a duct, similar to the one illustrated 
in Figure 5, are increased—sometimes to two, three, 
or four times the normal ranges. Ground echoes 
would be increased at the same time and might, in 
some cases, obscure partly, or even entirely, the 
echoes from incoming aircraft. 

When the radar is located within the duct, ranges 
on aircraft flying above the duct will be decreased 
only slightly, if at all. Often there may be a slight 
increase in effective ranges. If the angle of elevation 
of the aircraft is greater than 1 degree, the effects 
become inappreciable and failure to detect the target 
cannot be attributed to excessive refraction. 

If the duct does not include the radar within its 
boundaries, as, for example, when a duct forms below 
a high-sited radar, the effective ranges on surface 
craft may be either increased or decreased. Similar 
reasoning may be applied in the case of airborne 
VHF radio communication. Usually there is no very 
pronounced effect upon the signal strength when 
VHF communication is carried on between two 
aircraft, both flying above the duct. 

Interference between the direct rays and the rays 
reflected from the ground—resulting in the well- 
known lobe pattern of the coverage diagram—has 
not been mentioned. Under standard conditions the 
position of the lobes depends only on the wavelength 
used and the height of the radar above the ground. 
When a duct is present the lowest part of the coverage 
diagram may be strongly distorted. 

Coverage depends upon a variety of factors of 
which the most important are these: height of the 
top and base of the duct, amount of refraction in 
the duct, position of the transmitter relative to the 
duct, frequency (or wavelength) of the radar equip¬ 
ment, and height of the transmitter above ground. 

A coverage diagram for standard conditions is 
shown in Figure 6, diagram 1, with height strongly 
exaggerated. Only the lowest three lobes are shown, 
and the higher lobes appear compressed as compared 













182 


VARIATIONS IN RADAR COVERAGE 


altitude in feet 



The diagrams clearly indicate the great extension 
of ranges in the duct and also the moderate change 
in ranges—sometimes an extension, sometimes a 
reduction—above the duct. Another feature of some 
of these diagrams is the appearance of “skip-ranges.” 
A plane flying at an altitude of 500 ft, for instance, 
would be detected early under the conditions shown 
in diagrams 4 and 5. As the plane approaches, the 
echo will disappear from the scope and reappear only 
at a range less than 20 miles. Similar conditions will 
prevail for ground clutter. In diagram 3 there would 
be ground clutter close in and also from beyond 33 
miles but not from the space between. For conditions 
shown in diagram 5, there would be echoes from very 
remote ground targets but not from targets at inter¬ 
mediate ranges. 

A change in echo strength from day to day is not 
necessarily caused by the weather but might simply 
be caused by a variation in performance of the set. 
Cases have occurred where there was extensive trap¬ 
ping, but because of lowered set performance there 
was no corresponding increase in fixed echo strength. 
The set then will appear to be in good operating con¬ 
dition, and the operator will be deceived about ranges 
of detection for craft flying above the duct. Equip¬ 
ment for checking set performance is not usually 
available in the field. The change in intensity of 
nearby fixed echoes may be, in some cases, a measure 
of set performance, but in the absence of more 
elaborate checks this method can be misleading and 
should not be relied upon entirely. 

Failure of detection of targets is not necessarily 
due to weather influences. Electrical failure of the 
set or inadequate adjustment may be the difficulty 
and may be far more troublesome to identify than 
meteorological effects which should not be used as 
a “scapegoat” to be indiscriminately blamed for 
poor coverage. 

163 METEOROLOGICAL FACTORS 


Figure 6 . Standard and nonstandard coverage diagrams. 

to the lowest lobe. In diagrams 2, 3, 4, 5 the lower 
part of the same diagram is drawn as it appears 
under various conditions of guided propagation. The 
bottom part of the “standard” main lobe is shown 
by a broken line. The lines which separate the “blind 
zones” from the “detection zones” represent the 
range at which a medium bomber would just become 
visible to this particular radar set. 


The atmosphere is responsible for bending and 
duct formation. To understand the “why” of non¬ 
standard ranges of radar and radio with respect to 
the weather, it is necessary to consider the meteoro¬ 
logical factors involved. 

The strong refraction which results in guided 
propagation is caused by a rapid decrease of index 
of refraction with height within certain layers. The 
decrease depends upon distribution of moisture and 
temperature in the atmosphere, particularly in the 



























































METEOROLOGICAL FACTORS 


183 


lowest few hundred or thousand feet. Normally the 
temperature decreases with height in the atmosphere 
(at a rate of about 2°C per 1,000 ft), and the mois¬ 
ture decreases gradually with height. Under these 
conditions the propagation is of the standard type. 

Temperature may sometimes increase with height 
for a few hundred or thousand feet above ground 
and then, at greater heights, begin to decrease again. 
The vertical increase of temperature is called a tem¬ 
perature inversion. Sometimes a layer of moist air 
is found near the ground, and the air overlying it is 
very dry. There is then a rapid decrease of moisture 
over a short vertical distance; in other words there 
is a pronounced moisture lapse (see Figure 7). A 



Figure 7. Moisture variation aloft. 1. Moisture distri¬ 
bution with height in standard moist atmosphere. 2. 
Example of sharp moisture lapse (dry air overlying 
moist air) conducive to guided propagation. Mixing 
ratio is amount of moisture in a unit weight of dry air 
expressed as grams of water per kilogram of dry air. 

moderate or strong moisture lapse almost always will 
produce trapping, but a temperature inversion 
(except at low temperatures) will lead to trapping 
only if the moisture distribution is favorable. A 
combination of both effects within the same layer 
usually will produce trapping. 

The meteorological conditions to be found over sea 
and over land are quite different and must be con¬ 
sidered separately. 

Over Sea 

When warm, dry air flows over colder water, a 
temperature inversion will be established, and there 
will be evaporation into the lowest layers of the air, 
thus creating conditions of pronounced trapping. 
This weather condition is one of the most common 
causes of guided propagation. An example in point 
is the Mediterranean, which to the south, east, and 
west is surrounded by dry land masses producing a 
flow of dry, warm air over the water when the winds 


AIR OVER AFRICA 



AFTER PASSAGE ACROSS THE MEDITERRANEAN 



Figure 8 . Modification of air from Sahara Desert in 
passing over the Mediterranean. 


blow from these directions (see Figure 8). Similar 
conditions are often caused by westerly winds blow¬ 
ing from land to sea across the eastern boundary of 
a continent. Land and sea breezes may influence 
radar operation along a coast line. The wind direc¬ 
tion at a coast is often an important factor in deter¬ 
mining propagation conditions and should be closely 
watched. Whenever unusual propagation is observed 
by coastal radar stations, a record of prevailing winds 
at the time is very helpful in determination of future 
expected performance. 



Figure 9. Formation of temperature inversion over land 
due to nocturnal cooling. 

Over Land 

Temperature inversions are produced mainly by 
nocturnal or night cooling of the ground (see Figure 
9). Trapping may occur when the moisture distribu- 












184 


VARIATIONS IN RADAR COVERAGE 


tion in the lowest layers is such as to reinforce or at 
least not to counteract the effect of the temperature 
distribution, that is, when the moisture decreases 
not too slowly with height. Nocturnal cooling is 
greatest with clear skies and is quite small under 
an overcast. Hence guided propagation over land 
occurs at night almost exclusively with clear skies. 
This type of temperature inversion is strictly confined 
to land areas. It does not occur over the ocean because 
the sea temperature does not show appreciable daily 
variations. Temperature inversions caused by noc¬ 
turnal cooling are most pronounced over dry land 
(desert) but will occur almost anywhere over land 
with a clear sky and a not too humid atmosphere. 

Subsidence 

Another weather phenomenon favorable to trap¬ 
ping is subsidence. By subsidence is meant the slow 
downward motion, combined with horizontal spread¬ 
ing, of air above the lowest layers of the atmosphere. 
This process, which most frequently occurs in the 
area of barometric high, will produce temperature 
inversions; the subsiding air moreover becomes rel¬ 
atively much drier than the unaffected air below. In 
general the subsidence inversion is quite high (e.g., 
above 4,000 to 5,000 ft). In the light of present 
knowledge it appears that high subsidence inversions 
do not generally affect guided propagation when the 
sets are situated at low altitudes. It appears, how¬ 
ever, that such subsidence inversions might materi¬ 
ally affect communications or airborne radar search 
aloft. Lower subsidence inversions (1,000 to 2,500 
ft) along the southwestern coast of the United States 
are known to produce stable duct layers affecting 
radar coverage at low angles. 

Turbulence of the Air 

This has a distinct normalizing effect in that it 
tends to smooth out the temperature and moisture 
variations which are conducive to guided propaga¬ 
tion. Moderate to strong winds produce a turbulent 
layer extending normally to a height of about 4,000 
ft. The air is well mixed within this layer, and 
consequently the standard type of refraction prevails. 
Regions of a barometric low are characterized by 
strong to moderate winds and pronounced turbu¬ 
lence in the lower layers. In addition low pressure 
areas usually have overcast skies. Hence a barometric 
low will as a rule lead to propagation of the standard 
type. 


Frequency of Occurrence 

It is extremely difficult to estimate in general 
terms the frequency of occurrence of guided propa¬ 
gation, since statistical data are almost nonexistent 
at present except for very limited regions in Europe 
such as the North Sea. In the central Mediterranean 
during the summer months of 1943, ducts have been 
observed on 9 days out of 10. Frequent trapping has 
also been observed in some parts of the Pacific. At 
other times and places guided propagation might be 
an unusual occurrence, especially if the barometric 
pressure is generally low and the winds strong. It 
seems advisable to consult a weather officer with 
regard to any given locality. 

Measurements 

In order to determine weather’s influence upon 
radar in a quantitative way, the variation of refrac¬ 
tive index with height must be determined. This 
requires accurate knowledge of the temperature and 
moisture distribution in the lowest few hundred or 
thousand feet of the atmosphere. The ordinary 
radiosonde is not well adapted to measurements of 
this type because the measured points on an ascent 
are usually spaced several hundred feet apart. Among 
the methods which have been developed for this 
purpose during the past two years, the one most 
generally adopted uses a captive balloon (or kite) 
which carries aloft electrical temperature and moist¬ 
ure—measuring elements. These are connected to a 
meter on the ground by means of thin wires attached 
to the cable holding the balloon. This device permits 
measurements at intervals as closely spaced as 
desired. A psychrometer held out of the window of a 
slowly flying plane has been used with good success 
in the absence of more elaborate equipment. 

164 CLOUD ECHOES IN RADAR 

Cloud echoes (more precisely, precipitation echoes) 
are observed frequently on radar scopes. At times 
they have caused confusion by blotting out other 
targets. Their similarity, upon certain occasions, to 
actual targets have caused some difficulty in the 
interpretation of the signals. 

These echoes are caused by a reflection of the radar 
pulse from the raindrops in the clouds (or in rain 
storms). The amount of reflection increases very 
rapidly with frequency. Cloud echoes are quite 
exceptional below about 1,000 me. In microwave 




SUMMARY OF BASIC FACTS CONCERNING PROPAGATION AT RADAR FREQUENCIES 185 

1 


radar they first appeared as a nuisance, but more 
recently they have been put to practical use. In 
tropical climates they are very helpful for aerial 
navigation. 

Cloud echoes may be distinguished from other 
echoes by their fuzzy and diffuse appearance. Not 
all clouds show up on a scope with equal strength. 
The strength of the echo seems to depend primarily 
on the size of the water drops within the cloud or 
rain storm. Ordinary clouds such as form an even 
overcast (stratus clouds) are not usually visible on 
the scopes; the droplets that compose these clouds 
are so small that they reflect very little energy. 
Violent showers give intense echoes on the scopes. 
Storm echoes can be seen much farther than normal 
land targets, even under standard conditions, because 
of their great spread in the vertical direction. 

In discussing cloud reflections it must be clearly 
understood that there is no physical relation between 
cloud echoes and refraction; the mechanics of duct 
formation is not related to clouds, and with respect 
to the bending of radio waves a cloud is merely 
another airborne target. 

165 SUMMARY OF BASIC FACTS 
CONCERNING PROPAGATION AT 
RADAR FREQUENCIES 

1. Standard propagation results in a slight down¬ 
ward bending of the rays throughout the atmosphere, 
leading to an increase of the horizon distance com¬ 
pared to the geometrical value. It is taken into 
account operationally by using coverage diagrams 
with a % earth’s radius; on a diagram modified in 
this way the rays appear as straight lines. 

2. Guided propagation occurs almost exclusively 
in the lowest 2,000 ft above the ground and usually 
is confined to the lowest few hundred feet (except 
in warm climates). 


3. Superrefraction resulting in guided propagation 
or trapping is produced: 

a. By a pronounced decrease of moisture with 
height (moisture lapse), or 

b. By a pronounced increase in temperature 
with height (temperature inversion), and 

c. Particularly, by a combination of both of 
the above conditions. 

4. Of the meteorological conditions conducive to 
guided propagation or trapping, the most outstand¬ 
ing are: 

a. Over sea: flow of warm, dry air over colder 
water producing temperature inversions and 
evaporation into the lowest layers. 

b. Over land: nocturnal cooling of the ground 
with clear skies and calm air or light winds 
(if moisture distribution is favorable). 

c. Over both sea and land: low-level subsidence. 

5. Conditions in a barometric high, including calm 
and clear skies and especially low-level subsidence, 
favor trapping especially during the night (but do 
not necessarily produce it). Conditions in a baro¬ 
metric low, including strong winds, intense turbu¬ 
lence in the lowest layers, and overcast skies are 
conducive to standard propagation. 

6. When the transmitter is within the duct, radar 
range is increased for surface targets (ships) and air¬ 
craft flying in the duct. At the same time there is an 
increase in fixed echo strength and consequently in 
ground clutter on the scopes. This may be accom¬ 
panied by a change in the range of detection for 
craft flying above the duct. 

7. When the transmitter is outside the duct, the 
range may be either increased or decreased from its 
standard value. 

8. Effects of nonstandard propagation are negli¬ 
gible when the angle of elevation of the target is over 
1 degree. Failure of detection at such angles must be 
attributed to other causes. 












PART IV 


CONFERENCE REPORTS ON NONSTANDARD PROPAGATION 





































































































































































































































































Chapter 17 

TROPOSPHERIC PROPAGATION AND RADIO METEOROLOGY 


171 FUNDAMENTALS OF PROPAGATION 

17,1-1 Significance of Propagation Problems 

he central problem of short and microwave 
propagation (at frequencies greater than 40 to 
60 me) is the determination of accurate coverage 
patterns for a given transmitter. These patterns are 
usually calculated from electromagnetic theory and 
then may be checked by experiment. For communi¬ 
cation work the check is simple, namely, the estab¬ 
lishment of satisfactory communication. In the case 
of radar it is necessary to calibrate by time-consum¬ 
ing airplane flights. 

Experience has shown that actual coverage is not 
constant in time but suffers large variations which 
are caused by the changeable refraction of the at¬ 
mosphere. The variations in weather conditions that 
influence the refraction often are irregular and very 
rapid, and it is technically impossible to test all these 
conditions. Coverage diagrams, therefore, must be 
based on the physical principles of wave propaga¬ 
tion, assuming that the characteristics of the atmos¬ 
phere remain constant for reasonable periods. These 
principles are outlined here. 

At the present stage of technical development it is 
not always permissible to ascribe an observed varia¬ 
tion in coverage to changing atmospheric conditions. 
Variations in transmitter output or receiver sensi¬ 
tivity are always likely to be present to a degree 
sufficient to influence results considerably. In prac¬ 
tice it is often extremely difficult to tell these causes 
apart. In fact, investigations carried out with opera¬ 
tional radar equipment make it probable that an in¬ 
crease in surface coverage due to favorable conditions 
of refraction frequently passes unnoticed because of 
poor set performance. The coverage appears normal, 
while the set in reality is operating considerably be¬ 
low peak efficiency. 

A knowledge and understanding of the effects of 
weather upon propagation therefore will also be of 
help in checking set performance in the absence of 
suitable electrical equipment for measuring output 
and sensitivity. In dealing with coverage problems 
this double aspect of propagation phenomena should 
always be kept in mind. By a suitable analysis of the 

a By Columbia University 7 Wave Propagation Group. 


various factors determining coverage, and by an in¬ 
telligent understanding of their interplay, the re¬ 
sponsible officer may achieve a better control of the 
operational performance of his equipment. 

In tactical operations and in planning, a knowl¬ 
edge of the nonvariable factors affecting propaga¬ 
tion, such as dielectric constant and conductivity of 
the ground or sea, contours of the terrain, vegetation, 
etc., is equally important. Many problems concern¬ 
ing these factors cannot be considered in this manual 

17,1 ' 2 Factors Influencing Propagation 

This volume is confined to the propagation of 
waves within the troposphere and hence is not con¬ 
cerned with ionospheric propagation, which is re¬ 
sponsible for the long distance transmission of short 
waves (high frequency band). The higher the fre¬ 
quency above 30 me, the less frequently radio waves 
are returned to the earth by the ionosphere. Conse¬ 
quently very short radio waves are confined to the 
troposphere, and the treatment given here does not 
need to be supplemented by a study of the ionos¬ 
phere. Propagation in the lower atmosphere is called 
“tropospheric propagation” (see Figure 1). 



The main factors influencing the shape of a cover¬ 
age diagram under these circumstances are: (1) re¬ 
flection by the ground, (2) diffraction by the ground 
contour, (3) refraction by the atmosphere, and (4) 
guided propagation by superrefraction in the lower 
atmosphere. The present chapter deals mainly with 
refraction phenomena, but reflection and diffraction 
will be briefly considered. 

Refraction is influenced by the physical state of the 


189 




190 


TROPOSPHERIC PROPAGATION AND RADIO METEOROLOGY 


atmosphere, in which the distributions of the temper¬ 
ature, pressure, and humidity are the most important 
elements. With refraction, rays are bent, and the 
electromagnetic energy flows along the curved ray 
paths. A situation frequently realized in practice is 
that in which the curvature of the rays is independent 
of height above ground. This is known as standard 
refraction. The term standard propagation is used to 
designate propagation under conditions where the 
refraction is of the standard type. 

During the war years the increased number of ob¬ 
servations, which resulted from the world-wide use of 
radar, showed that, under certain weather conditions, 
radio field strengths may depart markedly from the 
values expected with standard refraction. These 
deviations are now known to be attributable to a 
stratification of the atmosphere which is predomi¬ 
nantly horizontal and is produced by vertical varia¬ 
tions in water-vapor content and temperature. Since 
these quantities control the index of refraction, and 
therefore the curvature of the rays, it follows that 
this curvature varies with the elevation above ground. 

Any stratification of the atmosphere tends to pro¬ 
duce a distribution of the radiated energy different 
from that which occurs in the standard atmosphere. 
Of particular importance is a type of stratification 
which results in a duct being formed in the atmos¬ 
phere. In this event, a portion of the wave energy 
may be guided horizontally along the duct and may 
be effectively ‘Trapped” within the duct’s upper and 
lower boundaries. This is known as “guided” propa¬ 
gation. The radiation energy may then travel to dis¬ 
tances far beyond the geometrical horizon, producing 
unusually long ranges for short wave receivers or 
radar targets. The phenomenon which tends to con¬ 
strain the wave energy to follow the duct is called 
“superrefraction.” When this occurs, the rays in pass¬ 
ing through the inversion layer in the upper part of 
the duct are bent downward with a curvature which 
exceeds that of the curvature of the earth. The 
regions covered by the inversion layer and the duct 
are illustrated in Figures 15, 20, 22, and 23. The dis¬ 
tribution of moisture and temperature in the atmos¬ 
phere, responsible for the formation of ducts, is dis¬ 
cussed in Section 17.3.1. 

As the stratification of the lower atmosphere that 
produces superrefraction is part of the weather, the 
prevailing meteorological conditions become of im¬ 
portance for problems of propagation and coverage. 
Meteorology as related to wave propagation is 
treated in Section 17.3. 


Reflection from the Ground 

A coverage diagram is a curve, or a set of curves, of 
constant field strength in a vertical or horizontal 
plane. The horizontal coverage diagram is deter¬ 
mined chiefly by the antenna pattern itself. In the 
vertical plane, however, tlie diagram depends pri¬ 
marily upon the interference between the radiation 
coming directly from the transmitter and that which 
is reflected from the ground or sea surface. This effect 
produces the lobe structure of the vertical coverage 
diagram. At the lobe maxima the two rays reinforce 
each other, while they cancel each other out, more or 
less, at the lobe minima. 

The propagation problem in its full generality 
leads to mathematical formulas of forbidding com¬ 
plexity. In order to understand the processes at work 
it is necessary to proceed in steps and gradually add 
refinements to the basic features of the problem. 

Consider first the field radiated from an antenna 
which is remote from the earth. This free space field 
decreases in strength in inverse proportion to the dis¬ 
tance, Ri f from the transmitter and varies with the 
angular position in accordance with the shape of the 
radiation pattern of the transmitting antenna. Let 
this free space field strength at any point at distance 
Ri be designated by Eq. 



Figure 2. Interference of direct and reflected'rays. 


If, instead, the transmitter is placed near the 
ground, as at T in Figure 2, the field at any point in 
space is produced partly by the direct wave (giving 
the free space field E 0 ) and partly by the wave which 
is reflected from the ground. The resultant field is 
given by the vector sum of the two component fields. 

The magnitude of the field strength of the reflected 
beam depends upon: 






FUNDAMENTALS OF PROPAGATION 


191 


1. The antenna radiation pattern, which gives the 
relative strength of the radiation field for different 
directions. 

2. The attenuation, proportional to 1/R 2 , resulting 
from the length of path R 2 of the reflected wave. 

3. The attenuation due to increased divergence of 
nearly parallel rays reflected from the curved earth. 
This is taken into account by the use of a divergence 
factor, D, which depends on range and heights of 
transmitter and receiver. 

4. The magnitude, p, that the coefficient of reflec¬ 
tion of the ground would have if the ground were 
plane. The reflection surface for a spherical surface, 
F, is then equal to pD. 

5. Irregularities of the earth’s surface which affect 
the reflection coefficient. 

If E 0 is the magnitude of the direct wave and F 
is the magnitude of the reflection coefficient, then 
the field strength of the reflected ray is FE 0 . 

The phase difference between the direct and re¬ 
flected fields is given by an angle 8 which is the 
sum of: 

1. The phase difference, >F, resulting from the 
difference in path length, R 2 —Ri; 

2. The phase difference, 0, suffered by the reflected 
wave upon reflection from the ground. 

The amplitude of the resultant field for a non¬ 
directive antenna is then given by GE 0} where 

G = Vl + F~ 2 + 2 F cos 5 (1) 

is the earth gain factor which is illustrated in Figure 3. 



Figure 3. Phase addition of direct and reflected rays. 

A curve drawn to represent the contour of constant 
field strength E = GE Q as a function of the range Ri 
and the angle of elevation (3 gives the vertical cov¬ 
erage diagram for that particular field strength. Cal¬ 
culation of these diagrams usually requires a con¬ 
siderable amount of detailed and laborious work. 

Consider the simple case of the vertical coverage 


diagram of a horizontal dipole antenna located above 
a plane earth in a homogeneous atmosphere. If the 
plane of Figure 2 is perpendicular to the dipole axis, 
the radiation pattern of the antenna is a circle of unit 
radius. The ratio, F 2 , of the magnitude of the re¬ 
flected wave to that of the incident wave is given by 
the magnitude, p, of the reflection coefficient. For 
propagation to distances that are great compared 
with the antenna elevation, the path lengths R 2 and 
Ri are not greatly different, and the attenuation due 
to path length is approximately the same for both 
direct and reflected waves. For this set of conditions 
the resultant field is E = GE 0 , and equation (1) 
reduces to 

G = Vl + p 2 + 2p cos S ' (2) 

In this form G is the plane earth gain factor and a 
plot of the curves E = GE 0 = constant as a function of 
range and angle of elevation gives the coverage dia¬ 
gram. It depends only upon the magnitude of the re¬ 
flection coefficient, the phase changes related to re¬ 
flection and to the difference in path length R 2 —R x . 

Since radar requires two-way transmission the re¬ 
ceived field strength is proportional toG 2 /R 2 i. Other 
modifying factors must, however, be introduced if the 
antenna and the target have directional radiative 
properties 

Both the magnitude of the reflection coefficient 
+F and the phase angle 0 by which the reflected 
wave lags behind the incident wave are functions of 
the frequency, the polarization of the radiation, the 
angle of grazing with the surface, the conductivity, 
dielectric constant, and roughness of the ground or 
sea surface. Figure 4 illustrates the variation of 
F{ = p) and 0 for reflection from a smooth plane sea 
surface for frequencies of 100 to 3,000 me, for both 
types of polarization, at different grazing angles. It 
may be noted that for horizontal polarization p is 
approximately unity and 0 nearly 180°, irrespective 
of the frequency and the magnitude of the grazing 
angle. This is the simplest situation to be encountered 
and most nearly approximates the idealized case of 
a perfect reflector with horizontal polarization. For 
this case p is exactly unity, and 0 is exactly 180°. 

For vertical polarization over the sea or either type 
of polarization over ground, both p and 0 depart 
widely from unity and 180°, respectively. Variations 
in these quantities greatly complicate the calculation 
of coverage diagrams. 

The reflection coefficient of microwaves is usually 
found to be small over land. This is essentially due to 







192 


TROPOSPHERIC PROPAGATION AND RADIO METEOROLOGY 




Figure 4. Phase and magnitude of reflection coefficient for sea water. 


irregularities of the land surface. When these irregu¬ 
larities are sufficiently small, reflection from land is 
found to be considerable. 

Since the receiver, or target, is usually located at a 
distance from the transmitter which is large in com¬ 
parison to the height above the ground, the direct 
and reflected rays are very nearly parallel, making an 
angel 0 with the horizontal (Figure 2). The reflected 
ray may be supposed to issue from an image trans¬ 
mitter T f , which is as far below the ground as the 


true transmitter is above it. The path difference be¬ 
tween the direct and reflected rays is equal to the 
distance T'A. By the figure this is equal to 2 hi sin 0, 
where hi is transmitter height. For small values of (3 
this is practically equal to 2/q/3 if /3 is measured in 
radians. The corresponding phase shift due to path 
difference is equal to 

= 2 M y . 

At the point of reflection the phase of a ray changes 


4 



































































































































FUNDAMENTALS OF PROPAGATION 


193 


discontinuously by the amount <j>, which is the phase 
angle of the reflection coefficient. For horizontal 
polarization, to again take the simplest case, the 
phase shift <j> at reflection is practically 180°, or 
7 r radians. (For vertical polarization, see Figure 4, </> 
is more complicated.) Adding the phase change 
corresponding to difference in path length, gives the 
complete phase change 8 in the form 

8 = +0 = 2h ij8 ^ + 7r (f or h orizontal polarization). (3) 
A 


earth, the refraction of the atmosphere, and diffrac¬ 
tion into the region below the line of sight. 



Figure 6. Use of equivalent ground plane. 


Maximum values of the earth gain factor G occur 
when 8 is an integral multiple of 2i r; minimum values, 
for odd integral values of 7r. The corresponding 
values of the angle of elevation 0 are given by 

_ A (m = 1, 3, 5, • * • (maxima) 

^ - 4/ii m (ra = 0, 2, 4, • • • (minima) 

(for horizontal polarization.) 

If the reflection coefficient F of the surface is 
assumed to be unity (see Figure 4) the plane earth 
gain factor G, from equation (2), reduces to 

G = 2 cos ^|) , 

which fluctuates between the limits of 2 and zero. 

The coverage diagram drawn for propagation over 
a perfectly conducting plane on horizontal polariza¬ 
tion is illustrated in Figure 5. As an example, consider 


tii 

o 



/=200 me, A =1.5 m, /*i = 30.5 m. The values of (3 
for the first three lobe maxima are 0.68°, 1.37°, and 
2.05°, and the maximum ranges are twice the free 
space values. The angles at which the minima occur 
lie half way between. The scale of vertical distances 
is greatly exaggerated compared with the horizontal 
scale. Coverage diagrams for the same frequency and 
transmitter height, but taking account of the earth’s 
curvature, are shown in Figure 24. 

Coverage diagrams for more complicated situa¬ 
tions must take into account, in addition to the 
factors already mentioned, the curvature of the 


When the ground is sloping, the above construction 
may be modified as indicated in Figure 6. For any 
specified lobe, determine approximately the part of 
the ground where reflection takes place. Draw a 
tangent to the ground in this region and determine 
the perpendicular projection of the antenna site on 
this plane (“equivalent ground”). Use the equivalent 
height thus determined in equation (3), and let the 
angle /3 refer to the plane of the equivalent ground. 
This procedure is also required when the transmitter 
and receiver or target are of comparable height so 
that the reflection point is not near the transmitter. 

When the transmitter is set up near a coast, the 
lobe pattern over the ocean will undergo periodic 
variations caused by the tides. Since, in equation (3), 
/3 is multiplied by hi, it follows that the lobes will be 
low at high tide and high at low tide. This phenom¬ 
enon may become very important for heightfinding 
sets. 

A more complicated case occurs if ground reflec¬ 
tion is not complete. Then p is less than| unity, and 0 
differs from 180°. In this event the lobes have max- 


UJ 

o 



Figure 7. Coverage diagram for incomplete reflection. 


ima which are less than twice the free space field and 
minima which never reach zero. The angular posi¬ 
tions of the lobes are changed somewhat, but the 
most noticeable change is found on the lower side of 
the first lobe. It is likely to lie at a lower elevation 
and reaches the ground at some distance from the 
transmitter (compare Figures 5 and 7). 







194 


TROPOSPHERIC PROPAGATION AND RADIO METEOROLOGY 


1714 Refraction—Snell’s Law 

The bending of rays in the atmosphere depends 
upon the refractive index n which is a function of the 
temperature, pressure, and moisture content of the 
air. The manner in which these quantities control the 
index of refraction is explained in Section 17.2.1. To a 
first approximation, assuming horizontal stratifica¬ 
tion of the atmosphere, the index may be considered 
to be a function only of height above the ground. The 
corresponding case, familiar in optics, is that of two 
media, such as water and air, with different refrac¬ 
tive indices Ui and n 2 (Figure 8A). If ai and a 2 are the 
angles between the rays and the plane of the bound¬ 
ary, Snell’s law of refraction states that 

Ui cos ai = n 2 cos a 2 . 

In the atmosphere the refractive index changes 
continuously with height. The simplest case, often 




Figure 8. A. Refraction at a sharp boundary. B. Re¬ 
fraction through a layer with variable n. 

encountered in practice, is that of a refractive index 
which decreases linearly with height. This is known 
as standard refraction. Snell’s law applies here also, 
since the atmosphere may be divided up into an in¬ 
finity of parallel boundaries, the change of refractive 
index from one boundary to the next being infinites¬ 
imally small. Instead of a sudden change of direction 
there is then a gradual change or bending of the rays 
(Figure 8B). Snell’s law may then be stated gen¬ 
erally as 

n cos a = n Q cos ao , 

where now n and a are continuous functions of height 
and the zero subscript on the right-hand side refers to 
any fixed reference level. The curvature of the re¬ 
fracted rays is downwards or upwards according to 
whether the refractive index decreases or increases 
with height. 


171,5 Refraction over a Curved Earth 

In reality the surfaces of constant refractive index 
are not planes but are concentric spheres about the 
earth’s center. In this case Snell’s law assumes a 
slightly different form. Instead of using angles re¬ 
ferred to the plane surfaces it is now necessary to 
refer the angles to horizontal planes tangent to 
spheres about the center of the earth (see Figure 9). 
The new form, as given in Section 17.4, is 

nr cos a = ano cos ao , (4) 

where r and a are values of the radius vector from the 
center of the earth to a point in the atmosphere and 



Figure 9. Refraction through a curved layer. 


to the earth’s surface, respectively, a now stands for 
the angle formed by the ray with a plane normal to 
the radius vector, ao and no are the values of a and n 
at the ground surface. 

If h is the height above the ground surface, so that 
r = h + a, the above equation may also be written 
in the form 

n ^1 + ^ cos a — n 0 cos a 0 . (5) 

h/a is a very small quantity, and n differs from unity 
by only a few parts in 10,000. Under these conditions 
n(l + h/a) may be replaced by n + h/a with neg¬ 
ligible error. The quantity n + h/a is called the 
modified refractive index, or the modified index for 
short. Equation (5) then assumes the form 

n + - J cos a = n 0 cos a 0 . (6) 

a) 

As a result of general agreement it is customary to 
use, instead of n + h/a, the symbol M defined as 
follows: 

M = (n + ~ 10 6 . (7) 

At the surface of the ground M reduces to 
M 0 =(»o-1) 10*. 


(8) 









FUNDAMENTALS OF PROPAGATION 


195 


Hence M is the excess of the modified refractive in¬ 
dex above unity, measured in units of one millionth. 
This unit is called an M unit [MU]. Values of M for 
the atmosphere lie in the range of 200 to 500. Cus¬ 
tomarily M is referred to simply as the modified 
index of refraction. 

Using the numerical value for the radius of the 
earth, 6.37 X 10 6 m (21 X 10 6 ft), the rate of increase 
of M with height, owing to the term h/a, is (1/a) 10 6 , 
which is equal to 0.157 MU per meter (0.048 MU per 
foot). As the result of a large number of experiments, 
carried out chiefly in the northern temperate lati¬ 
tudes, the rate of decrease with height of the re¬ 
fractive index has been found, on the average, to be 


= —0.039 MU per meter . (9) 

This is the rate of decrease assumed for the standard 
atmosphere. 

It will be noticed that the average rate of decrease 
of n with height is one quarter of the rate of increase 
of the term h/a which results from the curvature of 
the earth. The fact that these quantities are of com¬ 
parable magnitude is of great importance, as will be 
seen later. 

Consequently the vertical gradient of M for the 
standard atmosphere is 



which has the value 0.118 MU per meter (0.036 MU 
per ft). The value of M at any height, relative to the 
surface value M 0 , for the standard atmosphere, is 
equal to 

M — M 0 = 0.118 h; h in meters, 

M— M 0 = 0.036 h; h in feet. (11) 

171-6 Equivalent Earth Radius— 

Flat Earth Diagram 

An important conclusion may be drawn from 
equation (11). As will be shown in Section 17.2.4, 
dn/dh is the negative of the curvature of a ray in the 
atmosphere, and 1/a is the curvature of the earth. 
The algebraic sum of these two quantities (their 
numerical difference) is the curvature of the ray 
relative to that of the earth. The net result is this: if 


the earth is replaced by an equivalent earth with an 
enlarged radius equal to 4a/3 the rays may be drawn 
as straight lines. To state the result in another way: 
using the equivalent earth with radius equal to 4a/3 
corresponds to replacing the actual atmosphere, in 
which the index n decreases with height, by a homo¬ 
geneous atmosphere with an equivalent index n' 
which is independent of height (see Figures 10,11, 13, 
14, and 15). This transformation of coordinates great¬ 
ly facilitates the calculation and interpretation of cov¬ 
erage diagrams for the standard atmosphere. 

More generally, if the rate of change of n with 
height differs from the value —(1/4) (1/a) 10 6 MU 
per meter given above, which may be true in certain 
parts of the world, the equivalent earth radius de¬ 
parts from the value 4a/3. In general the equivalent 
earth radius is designated by ka. For a steeper drop 
of refractive index with height, k increases and be¬ 
comes infinite when the curvature of the ray is just 
equal to the curvature of the earth. 

In the general case, when k is not equal to 
equation (11) must be modified to the form: 

M — Mo = ^ 10 6 , 

= 0.157 | ; h in meters , 

= 0.048 ; h in feet , (12) 

to account for a linear moisture gradient correspond¬ 
ing to a different value of k. 

Since the change of the earth’s radius takes care of 
the variation of refractive index and substitutes a 
homogeneous atmosphere for the actual atmosphere, 
it follows that in a diagram in which the earth is 
given a radius ka, the radiation propagates along 



Figure 10. Ray curvature over earth of radius a in an 
actual atmosphere. 


straight lines. The difference is illustrated in Figures 
10 and 11. In Figure 10, which shows the true geo- 







196 


TROPOSPHERIC PROPAGATION AND RADIO METEOROLOGY 


metrical conditions, the radio horizon appears ex¬ 
tended as compared to the geometrical horizon, be¬ 
cause of the curvature of the rays. In Figure 11 the 
rays have been straightened out, but a line that was 
straight in Figure 10 appears curved in Figure 11. 

The value of % for A; is a good average for the at¬ 
mosphere in the middle latitudes. For particular 



Figure 11. Rays in a homogeneous atmosphere. Equiv¬ 
alent radius ka. 


atmospheric conditions the value of k may be con¬ 
siderably different. The moisture content of the at¬ 
mosphere is small at the low temperatures of the 
arctic regions and increases considerably with the 
higher temperatures of the tropics. However, the 


value of k depends more particularly on the manner 
in which the moisture content varies with height 
above the surface of the earth, and to a lesser extent 
on the distribution of temperature with height. 
Figure 12 has therefore been constructed to show the 
dependence of k on the gradient of relative humidity, 
measured in per cent per 100 m, for a series of surface 
temperatures varying between To— —30 C and 
To = +40 C.| It has been found convenient to plot 
1/k rather than k itself. The lines drawn correspond 
to the assumption of saturation humidity at the 
ground; if the humidity at the ground is less than 
100 per cent the correction read from the auxiliary 
table is added to the value of 1/k obtained from the 
graph. The standard temperature gradient of —0.65 
C per 100 m is assumed for all the curves. 

The curves of Figure 12 indicate that as the tem¬ 
perature increases, smaller and smaller values of rela¬ 
tive humidity gradients are required to produce 
changes in k of considerable magnitude. This should 
be of greater importance in the tropics where the 
moisture content is relatively high. 

Changing k from its standard value of % has an 
important influence on the strength of the field at any 



+ 4 +3 +2 -H to -I -2 -3 -5 -6 " 7 "8 

Figure 12. Graph: l/k versus RH gradient and temperature for 100 per cent RH at ground. 












































































































































FUNDAMENTALS OF PROPAGATION 


- 


197 


point in space. Though it is not easy to state the re¬ 
sult in general terms for any position, it is possible to 
evaluate the change in field strength near the surface 
(below 60 m altitude for 600 me and somewhat higher 
for lower frequencies) and well within the diffraction 
region, for moderate changes in k. Here the decibel 
attenuation below that for the free space field is de¬ 
creased approximately in the ratio &§. If, for in¬ 
stance, k changes from % to 8, the original decibel 
attenuation is to be divided by 3.3. To state the mat¬ 
ter another way, the range at which a given field 
strength is found will be increased approximately in 
the ratio &§. This has an important bearing on the 
problem of propagation for communication purposes 
in this region. 

It has been shown above that a linear variation of 
refractive index can be converted into a change of 
earth’s curvature. The reverse process is equally 
feasible: to eliminate the earth’s curvature by using 
a modified refractive index curve. This is a general 
procedure which involves no assumption about the 
variation of refractive index with height. From the 
equations in Section 17.1.6 it is seen that the effects 
of the earth’s curvature are equivalent to those of a 
refractive index increasing linearly with height at the 
rate of 1/a. Hence one effectively flattens the earth, 
thus eliminating the curvature effect, by adding to 
the refractive index the term h/a. In other words, 
the angles between a ray and the horizontal over a 
curved earth are the same as the angles between a 
ray and the horizontal over a flat earth when the re¬ 
fractive index n has been replaced by n + h/a. In 
practice, the quantity M defined by equation (7) is 
used. If M increases steadily with height, which is the 
case for the standard atmosphere, the rays appear 
curved upwards on a flat earth diagram, which is 
illustrated in Figure 13. 



Figure 13. Rays in a plane earth diagram. 


Summarizing, it is seen that three types of graphi¬ 
cal representations of a coverage diagram may be 
used. (These are illustrated in Figure 14 for the 
lowest lobe.) 

1. The true geometrical representation. With 




RADIUS ka 



k = oo 

Figure 14. Shape of lobes as affected by method of 
representation. 

standard refractive conditions the lobes appear bent 
downwards. Refractive index n decreases with height. 

2. The equivalent earth radius representation. 
Earth’s radius changed to ka (normally k=%). For 
standard refractive conditions the lobes appear 
straight. Equivalent refractive index n' is inde¬ 
pendent of height since the equivalent atmosphere is 
homogeneous. 

3. The flat earth representation. The earth’s sur¬ 
face and other surfaces of constant height have been 
flattened out. For standard refractive conditions 
the lobes appear bent upwards. Excess modified 
index M increases with height. 

The quantities n, n ', and M for these three cases 
are illustrated in the left-hand series of diagrams 
in Figure 15. 

1717 The Horizon—Diffraction 

From simple geometrical considerations it can be 
















198 


TROPOSPHERIC PROPAGATION AND R ADIO METEOROLOGY 


shown that two points at elevations hi and h 2 are 
within sight of each other when their distance is less 


field strength first increases rapidly and then oscil¬ 
lates between maxima and minima determined by 
the lobe patterns of the coverage diagrams. 


STANDARD ATMOSPHERE 


CURVED EARTH 
RADIUS Q 


CURVED EARTH 
RADIUS ka 
(HOMOGENEOUS 
ATMOSPHERE) 


'PLANE EARTH 
r ( MODIFIED INDEX 
CURVES) 


Figure 15. Types of index curves. 

than the horizon distance d h (Figure 16) given by 
d h = n/ 2kah i + y/Zkah 2 , (13) 



Figure 17. Diffraction and interference fields at height 
h*. Field strength at 50 statute miles over sea water in 
db relative to field at 1 m from transmitter. Horizontal 
polarization. Transmitter height 30 feet. 


where d h , a, and h are all expressed in the same units. 
For the particular value of k=%, 

d, = VTfhl + -v/mi, (U) 

where d h is measured in kilometers and h is in meters; 
and 

d„ = Vlhi + V2h*, (15) 

where d h is given in statute miles and h in feet. 

The field strength at different elevations h 2 (Figure 
16) for a given range varies in the manner illustrated 
in Figure 17. The field is given in decibels, relative to 
the intensity at 1 m from the transmitter, for a range 
of 50 miles over sea water for frequencies of 100, 200, 
500, and 3,000 me. The horizon elevation for this 
point is 888 ft. Above point P in Figure 16, is the 
interference region where, with increasing height, the 


with decreasing height to a minimum at ground 
level; the rate of decrease is larger for the higher fre¬ 
quencies. Neither the direct nor the reflected rays 
can penetrate into this region, which therefore, re¬ 
ceives radiation entirely by diffraction of the energy 
around the earth’s curvature. 

Radar targets are rarely visible when they are in 
the diffraction region. This is certainly true for air¬ 
plane targets. Yen' large targets, such as warships or 
islands, are occasionally visible in this region: but 
more often the detection of targets is caused by 
superrefraction. For communication work, on the 
other hand, the diffraction region is of importance, 
especially at the longer wavelengths. 

172 ATMOSPHERIC STRATIFICATION 
AND REFRACTION 


INTERFERENCE 
REGION 



Figure 16. Horizon distance. 


17 21 Origin of Refractive Index ^a^iations 

The variation with height of the index of refraction 
n controls the curvature of rays in the atmosphere. 
The value of n exceeds unity' by' only' a few hundred 













































































ATMOSPHERIC STRATIFICATION AND REFRACTION 


199 


parts in a million and may be computed from the 
following formula: 


(n - 1) 10 6 = 


79p 

~T 


11c , 3.8 X 10 5 c 

~jT H -- ( 16 ) 


in which n = index of refraction at height h above 
ground; 

p = barometric pressure of the atmosphere 
in millibars at height h. (1 mm Hg 
pressure = 1.334 mb); 

e = partial pressure of the water vapor in 
millibars (order of 1 per cent of p ); 

T = absolute temperature (°C + 273) at 
height h. 


In equation (16) the term lle/T is very small in 
comparison with the other terms and may, without 
serious error, be neglected. This simplification has 
been used in obtaining the values in the last two 
columns of Table 1 and in designing the nomogram, 
Figure 19. 

Workers in the field may prefer to use mixing ratio 
(practically equal to specific humidity) in place of 
the water vapor pressure. The relation is given by 

e = 0.00161 ps or s = , (17) 


where s is in grams of water per kilogram of air. 

The variation of n with temperature and relative 
humidity for an air pressure of 1,000 mb is illustrated 
in Figure 18. It is seen that the refractive index de¬ 
pends on humidity more critically than on tempera¬ 
ture. The dependence on humidity is greater at the 
higher temperatures where a given relative humidity 
represents a larger amount of water vapor. 

In practice it is customary to use the modified 
refractive index given by 


M = 




3.8 X 10 5 e 
T 2 


+ 0.157 h (h in meters). 



temperature in degrees c 


Figure 18. Relation of n to temperature and relative 
humidity. 

In order to compute M directly from temperature, 
relative humidity, and height data, the nomogram 
(Figure 19) has been constructed. Detailed instruc¬ 
tions for its use are given. 

The National Advisory Committee on Aeronautics 
[NACA] standard atmosphere commonly used in 
aeronautics assumes a sea level pressure of 1,013 mb 
( = 760 mm Hg) and a sea level temperature of 15 C, 
decreasing at a rate of 6.5 C per kilometer in the 
lower atmosphere. The NACA standard atmosphere 
is not concerned with the moisture content. In the 
actual atmosphere the moisture may vary between 
extremely wide limits, but as a typical value a rela¬ 
tive humidity of 60 per cent may be assumed as the 


Table 1 . Standard atmosphere with 60 per cent relative humidity. 



NACA standard atmosphere 


Moist standard atmosphere 



Dry air 

Dry air 

e(mb ) 

Moist 


Altitude, 

Temp, 

pressure, 

index, 

for 

air index, 

M = 

meters 

C 

mb 

(n - 1)10 6 

60% RH 

(n - 1)10 6 

(n + h/a - 1)10 6 

0 

15.0 

1013 

278 

10.2 

325 

325 

150 

14.0 

995 

274 

9.6 

318 

342 

300 

13.0 

977 

270 

9.0 

312 

359 

500 

11.7 

955 

265 

8.3 

304 

382 

1000 

8.5 

894 

251 

6.7 

283 

440 

1500 

5.2 

845 

240 

5.3 

266 

501 









































200 


TROPOSPHERIC PROPAGATION AND RADIO METEOROLOGY 


standard condition. This corresponds to a water 
vapor pressure of approximately 10 mb at sea level 
and a rate of decrease of water vapor pressure in the 
lower levels of about 1 mb per 1,000 ft. At higher 
levels the rate of decrease of the water vapor pres¬ 
sure is less rapid. These conditions are represented in 
Table 1 for the atmosphere up to 1,500 m. 

Both the dry and the moist standard atmosphere 
exhibit a very nearly linear increase of M with 
height. According to equation (12), 

M — Mo = ~ • 10 6 = 0.157^ ; h in meters . 

By using this formula in conjunction with Table 1 it 
is easily shown that k = % for the dry standard 
atmosphere, and k = % for the standard atmos¬ 
phere with a 60 per cent relative humidity. This 
value of k is the one commonly adopted in coverage 
diagrams corrected for standard refraction. 

Because of the great variability of the moisture 
content of the atmosphere with season, geographical 
location, etc., a moist standard atmosphere has a 
limited physical significance. The standard should 
rather be defined in terms of a fixed linear slope of 
the refractive index, and for this purpose the value 
k =% has been chosen. 

17 2 2 The Measurement of Refractive Index 

The lower atmosphere frequently is stratified by 
nonstandard distributions of temperature and hu¬ 
midity which vary rapidly and irregularly as func¬ 
tions of the height. The refractive index is then no 
longer linear but has a more complicated dependence 
on height, determined from equation (16). The strati¬ 
fication which is of particular importance in tropo¬ 
spheric propagation is found in the lower part of the 
atmosphere, that is, below about 4,000 to 5,000 ft 
and frequently in the lowest few hundred feet above 
ground. 

Since the variation in the atmospheric pressure 
gradient is small, interest is mainly centered in the 
dependence of the modified refractive index M on the 
temperature and humidity distributions. Methods, 
useful in the field, have been developed for obtaining 
rapid determinations of temperature and humidity in 
the lowest levels of the atmosphere. The ordinary 
radiosonde (radiometeorograph) is not well adapted 
for this purpose since it is usually designed to give 
data at levels about 100 m apart, which often is not 


close enough to reveal the significant details of the 
M curve. Consequently it has proved to be necessary 
to develop new instruments for this purpose. 

Several types of instruments have been designed 
which can be placed on towers, or carried by slow- 
flying airplanes or dirigibles or carried aloft by captive 
balloons or kites with wires connecting the tempera¬ 
ture and humidity elements to measuring or record¬ 
ing equipment located on ground or aboard ship. 

Some such measurements have been made with 
instruments using electrical methods in which dry 
and wet electrical resistance elements are connected 
into a circuit to give “dry bulb” and “wet bulb” 
temperatures. Another electrical method uses the 
same “dry” temperature element but, in place of 
the wet bulb, obtains a relative humidity measure¬ 
ment by using an electrolytic humidity element of 
the type employed in the U. S. Weather Bureau 
radiosonde. Hair hygrometers are definitely not 
suitable for this type of work on account of their 
lag in adjusting themselves to changes in relative 
humidity (of the order of 3 to 5 min for appreciable 
changes in humidity). 

Measurements made from airplanes have the 
advantage that it is possible to survey a compara¬ 
tively large area within a short time. This can be of 
great importance along coasts where conditions in 
the lowest levels of the atmosphere sometimes change 
rather rapidly with increasing distance from the 
shore. In the absence of suitable special equipment 
an ordinary psychrometer held out of the window of 
a plane will give quite satisfactory results in slow- 
flying planes, providing care is taken to keep the 
wet bulb sufficiently moist. When measurements are 
made from an airplane the height above the ground 
is determined for each measurement by means of 
the plane’s altimeter. Unless carefully done this 
introduces the possibility of considerable error. 

In another method captive balloons, kites, ordi¬ 
nary radiosonde balloons, and, occasionally, barrage 
balloons have been used to carry the measuring 
elements aloft. Ordinary captive balloons will work 
in wind speeds up to about 8 miles per hour; in 
higher winds kites or, occasionally, barrage balloons 
are used. Kites can be flown from boats even at low 
wind speeds or in calm weather. With this type of 
equipment the electrical measuring elements aloft 
are connected to an indicating or recording instru¬ 
ment at the ground or aboard ship by means of fine 
insulated wires that are wound around the cable 
holding the balloon. 



RELATIVE HUMIDITY 


ATMOSPHERIC STRATIFICATION AND REFRACTION 


201 



Figure 19. Temperature-relative humidity nomogram for computing M. 
















202 


TROPOSPHERIC PROPAGATION AND RADIO METEOROLOGY 


17.2.3 Types of Modified Index Curves 

A large number of meteorological soundings of 
the lower atmosphere have been carried out by 
several laboratories and Service units. From these 
measurements the modified index curves have been 
calculated as a function of height, and it has been 
shown that practically all these curves fall into one 
of the six types illustrated in Figure 20. 



Figure 20. Types of M curves. 


For the standard atmosphere the M curve increases 
with height as shown in curve I. For nonstandard 
atmospheres, the M curves will take one or another 
of the forms illustrated in curves la, lb, II, Ilia, 
and Illb. Of particular interest are those curves in 
which M decreases with height for a range of alti¬ 
tudes. (This decrease is the result of a sufficiently 
sharp decrease in n with height as illustrated in 
Figure 15.) In this event an inversion layer is formed 
in the atmosphere. 

Throughout the range of altitudes of decreasing 
M the curvature of the rays exceeds the curvature 
of the earth. Nearly horizontal rays which either 
originate in, or penetrate into, this layer are trapped, 
and, if the layer extends far enough, energy may be 
carried to distances far beyond the geometrical 
horizon. However, the region in which the waves or 
rays are trapped may have a thickness or depth 
exceeding that of the inversion layer. This region is 
known as a duct. Its precise definition may be taken 
from Figure 20. It is the strip between an upper 
minimum of the M curve and either the ground or 
the point where the vertical projection from the 
upper minimum intersects the M curve. There are 
two main types of ducts, the ground-based duct, 


illustrated by curves II and Illb, and the elevated 
duct, illustrated by curve Ilia. 

The height in the atmosphere at which the varia¬ 
tions in refractive index occur may vary from a few 
feet to several hundred or even a few thousand 
feet. These variations are likely to be found at fairly 
low elevations in cold climates and at the higher 
elevations in warm climates. The meteorological con¬ 
ditions which yield these various M curves are 
described in Section 17.3. 

The opposite effect occurs when the M curve takes 
the substandard form (curve lb in Figure 20). Here 
the lower portion of the M curve has a slope which 
is less than standard. In this event the rays in the 
lower atmosphere are bent downward to a lesser 
degree than in the standard atmosphere or may 
even be bent upward. Depending to some extent 
upon the elevation of the transmitter, the field 
strength in the substandard region may be reduced 
considerably below normal, even to the point of 
producing a radar and communication “blackout/’ 
If the M curve is steeper than average in the lowest 
layers, the transitional case arises (curve la). Here 
a slight change in the temperature and moisture 
distribution might lead to a curve of type II and 
a duct. 

17-2,4 Rays in a Stratified Atmosphere 

Nonstandard vertical variations of refractive index 
occur frequently in the lower atmosphere. In addi¬ 
tion there may be gradual variations in the horizontal 
direction. So far, the theory of propagation has not 
reached a stage where such horizontal variations can 
be taken into account. Unless otherwise stated it is 
always assumed that the stratification extends hori¬ 
zontally as far as the coverage of the transmitter 
and that the variation in the M curve is entirely 
vertical. Weather conditions often are sufficiently 
homogeneous horizontally to warrant this assump¬ 
tion, but there are exceptions, mainly near coasts 
(see Section 17.3). 

Only those rays are affected by the vertical varia¬ 
tions of refractive index in the lower atmosphere 
which leave the transmitter at a very small angle. 
Both theoretically and practically it has been found 
that the effects of nonstandard refraction are negli¬ 
gible for rays that leave the transmitter at an angle 
with the horizontal of more than about 1.5°. Rays 
that leave at an angle with the horizontal of less 
than 1.5°, and especially those emerging at angles 















ATMOSPHERIC STRATIFICATION AND REFRACTION 


203 


with the horizontal of 0.5° or less, are strongly 
affected by nonstandard refraction. This part of the 
transmitter radiation is of paramount importance in 
early warning radar and in communications. For 
such applications of radar as gun-laying or search¬ 
light control the effects of nonstandard propagation 
are usually negligible because the rays which reach 
the target have emerged from the transmitter at a 
fairly large angle with the horizontal. 

The progress of a ray through the stratified atmos¬ 
phere is described by SnelPs law, discussed in Section 
17.1.4. When the angle a between the ray and the 
horizontal is small 

9 

n O'¬ 
COS a = 1 — — , 

provided a is expressed in radians. 

Introducing this into SnelPs law for a curved 
earth, equation (6), noting that n + h/a = 1 + M- 
10“ 6 and neglecting second order quantities, it is 
seen that 

i (a 2 - ao 2 ) = (M - Mo)l(T 6 . (18) 

Since a is the angle which the ray makes with the 
horizontal it is equal to dh/dx, the slope of the ray. 
Solving equation (18) for a, 

a = ~ = V«o 2 + 2(M - M 0 )10 -6 . (19) 

These relations apply to any two levels provided a 
and ao are the angles at the levels to which M and 
M o refer. 


variations of the modified index. Although this ray 
tracing method is only an approximation of the true 
solution of the wave equation, it can be used, subject 
to certain limitations, for computing quantitatively 
the strength of the field. The approximation breaks 
down when neighboring rays cross each other and 
form caustics. 

The method may be illustrated by the case of 
standard refraction with k = %. As shown in Figure 
21, draw the M curve with a slope ka = 4a/3. Let 
the subscript 1 stand for the transmitter level (of 
height hi). Pass a vertical line through the corre¬ 
sponding point Mi of the M curve. Lay off the 
distance ai 2 /2 to the left of Mi for a particular ray, 
1, which emerges from the transmitter at angle cn 
with the horizontal. In order to make a and M 
comparable numerically, the factor 10“ 6 should be 
eliminated from equation (18) above. For this pur¬ 
pose a 2 should be measured in the same unit as M , 
that is, in 10 -6 radian. The distance between M and 
1 at any height h then is equal to (M — Mi) + ai 2 /2, 
and by equation (19) the square root of twice this 
quantity is equal to the slope of the ray at height h. 
Hence, ray 1 starting downward from the transmitter 
is bent more and more toward the horizontal as h 
decreases. At point P this ray becomes horizontal 
and from there on increases in slope with increasing 
height. 

Ray 1' starting upward from the transmitter at the 
same angle ai continues to curve upward more and 
more rapidly as the height increases. Ray 2 is the 



-► DISTANCE x 

Figure 21. Rays in the standard atmosphere. 

Equation (19) provides a technique for tracing the horizon ray which represents the limit to which rays 

paths of rays emitted by a transmitter at various can be directed by refraction. Beyond this lies the 

angles with the horizontal, and it indicates how their diffraction region where ray tracing cannot be used, 

passage through the atmosphere is controlled by the To study the field in the diffraction region the original 

















204 


TROPOSPHERIC PROPAGATION AND RADIO METEOROLOGY 


wave equation must be used. Ray 3 is reflected from 
the ground and in crossing some of the other rays 
produces the phenomenon of interference. In connec¬ 
tion with Figure 21 it must be emphasized that the 
height scale is tremendously exaggerated and that 
all the rays shown come from a small group which 
are propagated in a nearly horizontal direction. 

Sometimes it is convenient to express the path of 
the ray in terms of ray curvature. The true curvature 
of a ray as it appears on an un distorted (curved 
earth) diagram is different from the curvature exhi¬ 
bited by a ray on a plane earth diagram. The true 
curvature of a ray is given by 1/p, where p is the 
radius of curvature, and it can be shown that, for 
nearly horizontal rays, this is related to the gradient 
of n by 


1 _ _ dn 
p dh ' 


( 20 ) 


However, the relative curvature of the earth with 
respect to that of a ray is (1/a) — (1/p). Now let 
us set this equal to the curvature 1/ka of an equiv¬ 
alent earth. Then 


1 1 1 



( 21 ) 


and, introducing equation (20), ' 


k = 


1 



P 


1 a 


dn 

dh 


( 22 ) 


This amounts to a definition of k which is more 
general than the one introduced in Section 17.1.6 
but reduces to the latter when the index curve varies 
linearly with height. 

For a plane-earth diagram, M is used in place of n. 
Since 


M = 

dM 

dh 


(n + l- l)l0- , 

;(“h + ‘K 


Substituting the last equation into equation (22) 
gives 


k = - -^ 10 6 
a dM 


(23) 


and shows that k, in its most general form, is propor¬ 
tional to the slope of the M curve. Reference to 
Figure 20 shows that k assumes negative values for 
a range of altitudes whenever a duct is formed in 
the atmosphere. 


These relations may also be expressed in terms of 
m, where 


m = - (24) 

a 

is the ratio of the radius of curvature of a ray to 
the radius of the earth. From equation (22) it follows 
that 


\ + - = 1 . 
k m 


(25) 


Both k and m vary with height except in the special 
circumstance that the M curve is linear. Table 2 
gives a number of corresponding values of k and m 
and indicates their significance. 


Table 2. Relation of k and m. 


k 

i ? ® 

5 4 

I 2 

CO 

-2 -1 

m 

oo 6 5 

U.S. Brit. 

4 2 

1 

2 1 

3 2 


Moist 

Zero 

TN, i 4 


Standard 

stand- 

ard 

rela¬ 

tive 

curva¬ 

ture 

DUCl 

formation 


17.2.5 The Duct—Superrefraction 

When the M curve has a negative slope, k is 
negative; the curvature of the rays is concave down¬ 
ward on a plane earth diagram, and the true curva¬ 
ture of the rays is greater than the curvature of the 
earth. Hence rays which enter the duct under suffi¬ 
ciently small angles are bent until they become 
horizontal and then are turned downwards. This 
particular form of refraction is called superrefrac¬ 
tion. Such rays will be trapped in the duct, oscillating 
either between the ground and an upper level, or 
between two levels in the atmosphere. These condi¬ 
tions are illustrated by Figure 22 for the case of a 
ground-based duct and by Figure 23 for an elevated 
duct. 

The detailed construction of a ray diagram in the 
case of an elevated duct is shown in Figure 23. It 
is assumed, for illustration, that the transmitter is 
placed at the point which produces the maximum 
amount of trapping, and this point turns out to be 
located at the maximum of the bend in the M curve. 
The vertical line for Mi corresponding to hi is drawn 
as shown, and again the line 1 is drawn to the left 
of Mi at the distance ai 2 /2, to represent ray 1 which 












ATMOSPHERIC STRATIFICATION AND REFRACTION 


205 



Figure 22. Rays with a ground-based duct. 



departs from the transmitter at angle ai measured 
from the horizontal. As the ray proceeds outward 
and downward it is bent less and less, corresponding 
to the decreasing distance between the M and 1 
lines. Finally it reverses and rises to the height 
indicated. Ray 1 must therefore oscillate between 
the heights determined by the crossing of the M and 
1 lines. Ray 1' starting upward at the same angle a\ 
oscillates between the same height limits as ray 1. 

Rays 2 and 2' emerging at angle a v are the limiting 
rays which are trapped in the duct between the 
heights h t and h b . Beyond the horizon ray 3 and 
below the duct lies the diffraction region for this 
case. Ray 4 emerging at an angle greater than a v is 


not trapped but after reflection passes entirely 
through the duct. 

Ground-based ducts are likely to be found along 
coasts where warm, dry air from over land flows out 
over a colder sea. This situation, for instance, prevails 
in the summer months along the northeastern coast 
of the United States. Elevated ducts occur frequently 
along the southern California coast. 

An illustrative series of theoretical coverage 
diagrams as obtained by the ray tracing method 
described are collected in reference 448. A few of 
these diagrams are reproduced in Figure 24, for a 
frequency of 200 me and a transmitter elevation of 
hi = 100 ft, corresponding to an hi/\ ratio of approxi- 




























206 


TROPOSPHERIC PROPAGATION AND RADIO METEOROLOGY 


altitude 

FEET 

7000 



mately 20. The height scale is exaggerated in the 
ratio 40/1. Transmission over sea water is assumed. 
The coverage range is adjusted to “define the 
probable low-level zone of detection of a medium 
bomber with fair aspect by an SC-1 or SC-2 radar 
at 100-ft elevation. For SK radars and higher alti¬ 


tude installations, the diagrams are conservative. 
For SC and SA radars or for lower altitude installa¬ 
tions, they are optimistic.” 

Figure 24A shows the lobe structure for the 
standard atmosphere in which M increases 36 MU 
per 1,000 ft. It also shows the value of M — Mioo' r 
that is, the M curve is drawn so as to pass through 
zero at the transmitter elevation of 100 ft. On 
diagrams B through E the lower portion of the 
standard lower lobe is indicated by a dash-dot line. 
The blind zones are cross-hatched, and their boun¬ 
daries represent the calculated limits of detection. 
An interesting feature of these diagrams is the 
appearance, in some cases, of blind zones of consider¬ 
able range and altitude along the surface. These 
cause “skip ranges” for ground targets that are 
significant in operational problems. Ray diagrams 
were used in calculating the field strengths in 
Figure 24. 

The relative heights of the transmitter and the 
duct have an important bearing on the mechanism 
of transmission. The duct may develop entirely 
below the transmitter site or entirely above, or the 
duct may include the transmitter. With these alter¬ 
natives a variety of propagation conditions is 
possible. 

One of the important concepts of radiation theory 
is contained in the principle of reciprocity. This 
principle states that when a transmitter is at a point 
in space A, and the receiver at a point B, the 
received intensity is the same when they are inter¬ 
changed, the transmitter being at B and the receiver 
at A. (It is assumed in making this statement that 
the transmitter and receiver may be regarded as 
point sources.) Similarly, for radar the signal inten¬ 
sity remains unaltered if the positions of radar and 
target are interchanged. It is known that there are 
serious limitations to the reciprocity principle where 
ionospheric reflections are involved, but for shorter 
waves and tropospheric propagation the principle 
may be applied without restriction. By means of 
the reciprocity principle any coverage diagram may 
be used to obtain the field strength when the heights 
of the target and the radar are interchanged. 

From a study of such evidence on coverage 
diagrams as is available, it appears that (a) the 
effects of superrefraction are most marked when the 
transmitter lies in the duct; (b) they exist to a lesser 
degree if the transmitter lies below the duct: in 
particular no excessively long ranges for targets are 
then found above the duct—sometimes the ranges 


























































































ATMOSPHERIC STRATIFICATION AND REFRACTION 


207 


are extended slightly, other times slightly decreased; 
(c) for a transmitter above the duct no excessive 
changes in field strength occur below the duct—this 
can be deduced from (b) by using the reciprocity 
principle; (d) there is no appreciable superrefraction 
when the transmitter lies appreciably above the duct. 

For some time after the discovery of superrefraction 
it was thought that the concentration of radiative 
energy in the duct might result in a decrease of the 
amount of radiation above the duct and hence in a 
reduction of coverage there. The cases illustrated in 
Figure 24, at least, are not in accord with this 
presumption. In spite of the great increase in ranges 
in the duct the amount of energy trapped is small 
compared to the total energy of the radiation field. 

17 2 6 Wave Picture of Guided Propagation 

It must be realized that while ray treatments give 
accurate results under certain conditions, there are 
features of the propagation problem which can be 
satisfactorily discussed only on the basis of the 
electromagnetic wave equations. As an aid to under¬ 
standing the wave treatment the close analogy 
between the functioning of a duct and a hollow metal 
waveguide (or dielectric wire) may be used. In both 
cases the field which is being propagated may be 
represented as the sum of an infinite number of 
terms (modes). Each waveguide mode is propagated 
with a separate phase velocity and an exponential 
attenuation factor and has a field distribution over 
the wavefront that is independent of distance in the 
direction of propagation. 

In a metallic waveguide a finite number of modes 
are propagated with very small attenuation, while 
the remaining modes, infinite in number, have 
attenuations so high that they are, practically speak¬ 
ing, not propagated at all. The same division of 
modes into those that are freely propagated and 
those that are highly attenuated is found for duct 
propagation. In the duct, however, the difference 
between the two types of modes is less pronounced 
than in a hollow metal tube. 

As the frequency is decreased, the number of 
transmission modes decreases both for the hollow 
metal tube and the duct until the cutoff frequency 
is reached, below which neither serves as a wave¬ 
guide. For the case of simple surface trapping (Section 
17.2.3) the following formula gives the approximate 
maximum value of the wavelength for which guided 
propagation inside the duct can still take place: 


Amax = 2 .5d \/A M • 10~ 6 . 

Here d is the height of the top of the duct above the 
ground in the same units as X max , and AM is the 
decrease in M inside the duct. This relationship is 
represented in Figure 25 where, it should be noted, 



50 100 500 1000 

d IN FEET 


Figure 25. Maximum wavelength trapped in simple 
surface trapping. Duct width d in feet. AM is total 
decrease of M in duct. 

the duct width is given in feet and the wavelength 
in centimeters. When the wavelength exceeds the 
critical value obtained from this graph, guided 
propagation is no longer to be expected. M curves 
of different shapes will require slightly different 
numerical factors in the formula. 

The main difference between the modes is found 
in the vertical distribution of field strength. The first 
three modes for a simple ground-based duct are 
illustrated in Figure 26. The lowest mode has 




FIELD STRENGTH — 

Figure .26. Vertical distribution of field strength for 
first three modes in a duct. 



























































208 


TROPOSPHERIC PROPAGATION AND RADIO METEOROLOGY 


approximately % of a cycle of an approximate sine 
wave, followed by an exponential decrease. Higher 
modes have multiples of half cycles added to the 
sinusoidal part. 

How these modes must be combined to give the 
total field strength and its vertical distribution is a 
question which depends on the height of transmitter, 
the distance out to the point where the total field 
strength is to be obtained, the rate of attenuation of 
each mode as a function of the distance, and its 
phase velocity. Since the attenuation and the phase 
velocity are different for the various modes, the 
vertical distribution of the total field changes with 
the distance from the transmitter, and the number 
of modes composing the total field decreases with 
increasing distance. 

17.2.7 Reflection from an Elevated Layer 

This phenomenon has been studied extensively at 
San Diego. The meteorological situation there is 
rather unique in that the warm and extremely dry 
upper air overlies a cooler and very moist lower 
stratum. The transition between the two layers is 
very sharp. This gives rise to an elevated duct of 
the type exhibited by the M curves of Figures 24D 
and 24E. Often the reversal of the M curve takes 
place over an even narrower interval of height than 
shown in these graphs. In such cases there is a 
reflection analogous to the reflection of waves at a 
true discontinuity between two media and which 
cannot be accounted for by the bending of rays. 

At an interface between two media of different 
refractive indices there is partial reflection of radia¬ 
tion for any angle of incidence, but when the 
phenomenon (partial reflection and partial trans¬ 
mission) takes place in a layer of finite thickness, 
the reflected radiation is appreciable only at angles 
near grazing (less than 1° under the conditions found 
at San Diego). Furthermore, other things being 
equal, the reflection coefficient increases with increas¬ 
ing wavelength. This feature distinguishes the reflec¬ 
tion by a layer from the duct effects produced by 
this layer, as the latter generally tend to become less 
pronounced for longer waves. The reflection gives 
rise to an additional field strength near the ground, 
often well beyond the optical horizon. 

Transmission experiments carried out at San Diego 
at frequencies between 50 and 500 me gave results 
that are explained satisfactorily on the basis of 
reflections of the type just described but not on the 


duct theory. Thus most of the ducts caused by 
reversals of the M curve of the type shown in Figure 
24D will be beyond cutoff for a frequency of 50 me, 
according to Section 17.2.6. No guided propagation 
should therefore be expected, whereas the observed 
field at the receiver, located well beyond the optical 
horizon, was consistently very high. 

At a frequency of 500 me the reflection is found 
to be highly critical with respect to the angle of 
incidence at the reflecting layer. When meteorological 
conditions are such that the layer is high (3,000 to 
4,000 ft), and therefore the angle of incidence large, 
the intensity of the reflected radiation is found to 
be very low; when the layer forms at a low level 
(a few hundred feet only) the reflected radiation 
becomes very strong. This behavior agrees with the 
predictions of electromagnetic theory. 

So far, the experiment at San Diego is the only 
instance where a clear-cut case of reflection by an 
elevated layer has been found, although indications 
of similar effects have been observed elsewhere. 
Whether or not this phenomenon will occur at other 
places in or near the subtropical belt is not conclu¬ 
sively known since our knowledge of meteorological 
conditions in these climates is far from complete. 
If it does occur, it will obviously be of great opera¬ 
tional significance. 

17,2,8 Operational Applications 

Radar 

Ground radars have experienced most of the effects 
of propagation in nonstandard atmospheres so far 
observed operationally. Phenomenal ranges on ship 
and low-flying airplane targets have been observed, 
especially in the Mediterranean area, the Arabia- 
India area, in Australia, and the Southwest Pacific 
theaters. In the United States and Europe ground- 
based ducts over land have occasionally produced 
fixed echo clutter seriously interfering with the 
plotting of aircraft targets over land. This ground 
clutter interference is especially troublesome with 
microwave early warning sets plotting targets over 
land. On ground radars with high pulse repetition 
rates, echoes from large distances frequently return 
on the second or later traces. Such echoes interfere 
with first sweep echoes and sometimes are misinter¬ 
preted as having ranges appropriate to the first 
sweep, with serious tactical consequences. 

One of the most serious operational consequences 
of superrefraction is a secondary effect, that of 




ATMOSPHERIC STRATIFICATION AND REFRACTION 


209 


misleading operators as to the overall performance 
of the equipment. Long-range echoes caused by 
superrefraction have frequently been assumed to 
indicate good condition of the equipment, when 
precisely the opposite is actually the case. The 
phenomenon of superrefraction does not, however, 
in the same degree invalidate the measurement of 
signal-to-noise ratio of nearby echoes, as a criterion 
of relative overall set performance. Field strengths 
from nearby objects well within the optical horizon 
are far less subject to propagation variations. Echo 
strengths (signal-to-noise ratio) from nearby objects 
are still considered a good relative index of overall 
performance, provided that easily recognized echoes 
can be measured which are not sensitive to very 
small changes in the radar frequency. There are 
other sources of echo fluctuations such as the motion 
of objects (trees, towers) caused by the wind (import¬ 
ant at wind speeds above 15 miles per hour). Great 
care is needed in the choice of fixed echo “standards” 
so that they are kept free of the effects enumerated. 
Sometimes artificial echoing objects are constructed 
of flat mesh screens perpendicular to the beam in 
order to secure suitable echoes which are not 
frequency sensitive. The extreme variability of long- 
range fixed echoes emphasizes the operational need 
for reliable test equipment for making quantitative 
tests on the components as well as on the overall 
performance of the equipment aspects of radars, as 
distinct from propagation effects. 

In addition to the direct electrical checks on set 
performance there are a number of ways of making 
sure indirectly whether any failures of detection by 
radar may be due to a deformation of the coverage 
pattern by superrefraction. In the first place, super¬ 
refraction rarely affects detection at angles of eleva¬ 
tion above about 1.5°. Any irregularity at higher 
angles must be attributed to other causes. Even 
between 0.5° and 1.5° failures of detection are excep¬ 
tional and occur only where there are very strong 
ducts. A clue to the probability of occurrence of such 
conditions can be ascertained from a study of the 
primary meteorological effects which cause them; 
and even with only a moderate amount of meteoro¬ 
logical information it is usually possible to make an 
estimate of this probability. Such superrefractive 
conditions almost invariably show up in intensified 
and extended ground echoes (ground clutter on the 
scopes) and, in case of an overwater path, in extended 
ranges of ship detection. A record of meteorological 
data will be very helpful in deciding, after the fact, 


whether any specific failure of aircraft detection 
might have been ascribed to weather. Even if this 
is probable, there are, of course, a number of other 
operational causes that might be responsible rather 
than the weather. 

Experience gained in England indicates that the 
technique of forecasting whether or not superrefrac¬ 
tion occurs is, on the whole, fairly successful, but 
there are still many occasions when the predictions 
are not fulfilled. It has been intimated that in 
England this was due, at least partly, to variations 
in the sensitivity of the 10-cm set used; when the 
set is not at peak efficiency, maximum ranges of 
surface targets appear shortened, and the coverage 
in the duct may be reduced to a value corresponding 
to standard conditions. 

A major problem in any early warning radar 
system is that of heightfinding by means of maximum 
ranges. On this it is difficult to make general state¬ 
ments. The method of heightfinding usually employed 
in long-range radar work consists in using the boun¬ 
dary of the lowest lobe as a height indicator, assum¬ 
ing that when the target is first sighted it has just 
entered the lowest lobe. When superrefraction is 
present, the height estimated in this way can be 
seriously in error. It may be too high if the enemy 
is flying in the duct, so that he is discovered earlier 
than he would be normally; or it may be too low if 
the enemy is flying in the region above the duct and 
so he is discovered later than he would be under 
standard atmospheric conditions. Here, again, it 
should be possible to find out whether repeated 
errors in height determination are the result of 
superrefraction or whether they are due to faulty 
calibration or to other features not related to the 
weather. Other methods of heightfinding, such as 
are used in fighter control and control of antiaircraft 
fire, are usually carried out at angles of elevation too 
large to be affected by nonstandard types of atmos¬ 
phere. 


VHF Communications and Navigational Aids 

The extension of the maximum range of very high 
frequency [VHF] navigational aids has already been 
mentioned as an important consequence of super¬ 
refraction. Similar extensions of communication 
ranges of VHF radio sets also occur. Because VHF 
air-to-ground communications are relied upon only 
for comparatively short-range communications, this 



210 


TROPOSPHERIC PROPAGATION AND RADIO METEOROLOGY 


extension of the normal range by atmospheric 
conditions is important primarily from a security 
standpoint. It must always be borne in mind that 
transmissions on YHF may frequently be propagated 
hundreds of miles beyond the normal limiting range 
and are subject to enemy interception. Superrefrac- 
tion has also been observed to cause very objection¬ 
able mutual interference between two control towers 
attempting to use a common VHF channel, although 
the distance between the airports was great enough 
to prevent serious mutual interference under normal 
conditions. Point-to-point VHF radio links are also 
affected by refraction, over longer paths than optical. 


Radio Countermeasures 

The laws of radio propagation enter into the 
problem of jamming the enemy communication and 
radar equipment. Since it is rarely possible to locate 
the jamming transmitter coincident with the enemy 
transmitter whose signals it is desired to 'mask, the 
efficiency of propagation of the signals from the 
enemy transmitter relative to those of the friendly 
transmitter enters into the problem. This has been 
worked out in detail for the standard atmosphere. 
When conditions are not standard, however, the 
effectiveness of the enemy transmitter, as determined 
for standard conditions, no longer applies. A case of 
special interest occurs when an airborne jamming 
transmitter is used as a countermeasure against an 
enemy radio communication link operating between 
two points on the ground. If the meteorological 
situation is such as to be favorable to formation of 
a ground-based duct the enemy signals may be 
propagated with small attenuation, whereas the 
signals from the jamming transmitter may be unaf¬ 
fected or even weaker than would normally be 
expected. 

Plans for the employment of ground-based jammers 
against enemy radio and radar systems should take 
into consideration the ability of atmospheric refrac¬ 
tion to increase, or occasionally to decrease, the 
signal propagated to the enemy’s installation for 
jamming purposes. However, there has been only 
limited use of ground-based jamming so far. Unin¬ 
tentional mutual jamming has occurred between the 
spaced radar sets of a coastal system on the same 
frequency, where nonstandard propagation condi¬ 
tions caused strong signals to be propagated between 
normally noninterfering radars. 


17 3 RADIO METEOROLOGY 

17,31 Temperature and Moisture Gradients 

Section 17.3 is devoted to a survey of the meteoro¬ 
logical conditions which produce the various types 
of propagation described in the preceding sections. 
This brief outline is not intended to replace the 
assistance of a professional meteorologist in analyzing 
short and microwave propagation problems; but by 
familiarizing radar or communications personnel with 
the fundamental physical processes of low-level 
weather it may open the way toward a more fruitful 
consultation with the meteorologist. 

Duct formation is the most important phenomenon 
for which a detailed knowledge of the physical state 
of the lower atmosphere is required. Whenever a 
duct is formed, M decreases with height within a 
certain height interval. Since, according to Sections 
17.1.5 and 17.2.1, M = (n - 1) • 10 6 + 0.157fc,the 
existence of a duct presupposes that the refractive 
index n decreases with height over at least a limited 
range of altitudes at a rate more rapid than 0.157 
MU per meter. Such a decrease can be produced by 
two different meteorological conditions. 

1. A rapid increase of temperature with height. 
This temperature inversion must be very pronounced 
in order, by itself, to produce a duct. In practice, a 
temperature inversion contributes to duct formation 
when accompanied by a sufficiently strong moisture 
lapse. 

2. A rapid decrease of humidity with height desig¬ 
nated as a “steep moisture lapse.” 

When ducts are produced by only one of these 
causes, they may be designated as “dry ducts” and 
“wet ducts,” respectively. In the general case a 
temperature inversion and a moisture lapse cooperate 
in producing a duct, but one of the two factors will 
be preponderant, thus facilitating the analysis of the 
meteorological problem. 

Whether or not a duct occurs under given meteoro¬ 
logical conditions and what the rate of change of M 
is inside the duct may be determined by means of 
the diagram, Figure 27. (This discussion is presented 
for the purpose of illustrating the importance of 
temperature and moisture gradients. The technique 
more readily usable in practice is to compute the 
values of M at various altitudes directly from tem¬ 
perature and relative humidity data with the aid of 
Figure 19.) The abscissa in Figure 27 is the rate of 
decrease of humidity with height { — de/dh), where e 
is the water vapor pressure in millibars, (e can be 



RADIO METEOROLOGY 


211 



-——IN MB PER 100 METERS 

dh 

Figure 27. Temperature and humidity gradients. 


found from meteorological tables when relative 
humidity and temperature are known.) The ordinate 
is the rate of increase of temperature with height 
(i dT / dh ). The slanting lines represent various values of 
temperature and relative humidity at some particular 
height h. The lines passing through the same point 
at the upper right of the diagram correspond to the 


same mean temperature; lines of different slopes 
represent different mean relative humidities. 

In order to determine the rate of change of M at 
a given level, find the point in the diagram corre¬ 
sponding to the actual rates of change of moisture 
and temperature. Also pick out the straight line 
representing the actual mean values of temperature 








































212 


TROPOSPHERIC PROPAGATION AND RADIO METEOROLOGY 


and humidity in the layer considered. If the point 
is at the lower right relative to this straight line, M 
decreases with height in the layer chosen; that is, a 
duct exists. If the point is at the upper left of the 
straight line, M increases with height and there is 
no duct. 

The rate of change of M, (dM/dh ), may be 
obtained from the diagram by measuring the hori¬ 
zontal distance from the point to the line and 
multiplying by the function of the temperature / (T) 
given in the table on Figure 27. The result is the 
value of dM/dh, the rate of change of M, in M units 
per 100 m. This quantity is negative when the point 
is to the right of the line and positive when the point 
is to the left of the line. 

It is seen at once from the diagram that for small 
values of the moisture lapse an extremely steep 
temperature gradient is required in order to produce 
a duct (lower left part of the diagram). In cold air 
such as is found in the arctic the total moisture is 
small, and hence the moisture gradient will in general 
be quite small. Ducts will then only occur when a 
very strong temperature inversion exists. 

Strong temperature inversions occur only under 
special meteorological conditions which will be 
discussed below. Ordinarily the temperature of the 
air decreases with height ; and this will put our 
representative point into the upper part of Figure 
27. A duct can then exist only when the moisture 
lapse is large enough, so that the representative 
point falls to the right of the appropriate slanting 
line. Such conditions are common in the lower 
atmosphere. This leads to a wet duct, which is 
determined almost completely by the moisture lapse. 

17,3,2 Physical Causes 

of Stratification—Turbulence 

There are three basic meteorological factors which 
tend to modify the temperature and moisture distri¬ 
butions in the lowest layers of the atmosphere. These 
are: (1) advection, (2) nocturnal cooling (over land), 
and (3) subsidence. 

Advection is a meteorological term used to desig¬ 
nate the horizontal displacement of air having 
particular properties. Advection is of great interest 
in propagation problems particularly because it leads 
to an exchange of heat and moisture between the air 
and the underlying ground or sea surface and thus 
affects the physical structure of the lowest layers. 

Nocturnal cooling over land is caused by a loss of 


heat from the ground by infrared (heat) radiation. 
The cooling of the ground is communicated to the 
lower layers of air and leads to the establishment of 
a low-level temperature inversion. 

Subsidence means a slow vertical sinking of air 
over a very large area. It is most likely to be found 
in regions where barometric Highs are located. 
Subsidence tends to produce a temperature inversion 
and also produces very dry air which, spreading out 
over a humid surface, creates a situation which is 
favorable for the formation of a duct. 

The processes (1) and (2) change the physical 
characteristics of the air through transfer of heat 
or moisture between the air and the underlying 
surface of the ground or sea. The operating factor 
in this exchange is turbulence. The main features 
of turbulence in the lower atmosphere are outlined 
briefly below. 

Convection occurs spontaneously whenever the 
decrease of temperature with height exceeds a value 
of about 1 C per 100 m. This convective condition 
is usually produced as a result of the heating of the 
ground by the sun’s rays. Even with a cloudy sky 
the diffuse daylight often is strong enough to produce 
moderate convection. On a hot summer day convec¬ 
tion over land extends to great heights. Convection 
mixes the air thoroughly and thus causes a uniform 
distribution of moisture and a uniform decrease of 
temperature with height of about 1 C per 100 m. 
Hence even moderate convection tends to produce a 
smooth M curve which varies linearly with height. 
Standard conditions may therefore be assumed to 
prevail on clear summer days (and not infrequently 
on clear days in the cooler seasons) from the hours 
of late morning until late afternoon, during which 
time convection is most active. 

Frictional turbulence occurs frequently in the lower 
atmosphere even in the absence of convective condi¬ 
tions. It is caused by the wind and requires the 
presence of at least light winds, but with moderate 
or strong winds the effect is more pronounced. In 
conditions of calm or with a gentle breeze, frictional 
turbulence is confined to the lowest strata. Moderate 
or strong winds develop a layer of intense turbu¬ 
lence, caused by friction of the air at the irregularities 
of the ground. This layer is usually quite well defined 
in height and extends to an average elevation of 
about 1,000 m over land. Over a relatively smooth 
sea where friction is small the height of the layer is 
much reduced. In this frictional layer the air becomes 
thoroughly mixed; the vertical temperature gradient 



RADIO METEOROLOGY 


213 


caused by convection is about —1C per 100 m, and 
the moisture lapse is steady and rather small. 
Standard refraction will therefore prevail when winds 
are moderate to strong over land, and over the ocean 
also when the winds are sufficiently strong. 

Temperature inversions occur when the temperature 
of the surface (sea or land) is appreciably lower than 
the temperature of the air. The transition from the 
ground temperature to the free air temperature takes 
the form shown in Figure 28. The heat and moisture 



Figure 28. Air temperature versus height for an 
inversion. 

transfer caused by turbulence in a temperature inver¬ 
sion is less simple than that in a frictional layer. 
The turbulent processes active in inversion regions 
are highly complex and are not yet very well 
explored. It is known, however, that the intensity of 
the vertical transfer of heat and moisture is greatly 
reduced as compared to the rate of transfer with 
frictional turbulence. The reduction is the more 
pronounced, the steeper the vertical increase of tem¬ 
perature; in a steep inversion the rate of transfer 
may be many times less than in a frictional layer. 
This tends to produce a vertical stabilization of the 
air layers in the inversion region. As soon, therefore, 
as a temperature inversion has begun to form, the 
rapid mixing in the lowest layers, usually effected 
by frictional turbulence, stops and is replaced by a 
much more gradual diffusion. 

Assume now, for instance, that the rate of diffusion 
has become so slow that the transfer of moisture over 
a height of a few hundred feet takes many hours or, 


perhaps, a day or two. When the air in the inversion 
is dry to begin with and flows over ground capable 
of evaporation (the sea or moist land) there will be 
established, in such an air mass, a steep moisture 
lapse, since the water vapor that has been taken up 
by the air near the ground will only gradually diffuse 
into the dry air aloft. Conditions are then favorable 
for the formation of an evaporation duct, in addition 
to whatever tendency toward duct formation may 
be caused by the temperature inversion itself. 

17 33 Advective Ducts—Coastal Conditions 

Advective formation of ducts may occur both over 
land and over sea, but this process is most important 
over the ocean near coasts. The most common illus¬ 
tration is that of air above a warm land surface 
flowing out over a cooler sea. Over the land the air 
will usually have acquired a convective or nearly 
convective temperature gradient of — 1 C per 100 m. 
When this air flows out over the cool water surface, 
a temperature inversion is rapidly formed which 
grows in height as the process of turbulent transfer 
progresses. The temperature inversion does not, in 
itself, give rise to a pronounced duct because the 
effect of a temperature gradient upon the M curve 
is relatively small; but when the air is dry, evapora¬ 
tion from the sea surface takes place simultaneously 
with the heat transfer, and a moisture lapse rate is 
established in the lowest layers. The combination of 
temperature inversion and moisture lapse rate is 
most favorable for the formation of a duct off shore. 

The gradual formation of this type of duct is 
illustrated in Figure 29. This shows M curves, corres- 



M-Mf> 

Figure 29. Development of duct off coast. Initial state 
corresponds to air at coast line. }/i hr, }/% hr, etc., refer 
to time air has been over water. Initial conditions for 
this set of curves: unmodified air To — 32 C, e = 12.3 
mb; water T w = 22 C, e w = 26.5 mb saturation. 

ponding to the simple surface type of trapping (see 
Figure 20, curve II) for a series of time intervals 






































214 


TROPOSPHERIC PROPAGATION AND RADIO METEOROLOGY 


(and distances) as the air moves out over the water. 
The top of the duct is given by the elevation of the 
minimum value of the M curve. It will be noticed 
that the duct acquires a maximum depth some time 
after the air has touched the cold water surface; 
thereafter the depth decreases. The cause of this 
behavior is found in the progressive decrease in 
moisture and temperature differences which is the 
final result of the diffusion process. Thus the final 
stage of this transformation is an air mass whose 
temperature and moisture distributions are in equi¬ 
librium with the underlying water surface and no 
longer show a rapid variation with height. 

Duct formation in such a case depends on two 
quantities: (1) the excess of the unmodified air 
temperature above that of the water and (2) the 
humidity deficit, that is, the difference of the satura¬ 
tion vapor pressure corresponding to the water tem¬ 
perature minus the actual water vapor pressure in 
the unmodified air. If these quantities are large, 
especially the humidity deficit, a duct will develop. 
A great variety of local conditions may, however, 
be encountered in problems of this type, and empiri¬ 
cal rules developed for one locality may not at all 
apply to others. 

Advective processes may also occur over land, but 
the conditions required for duct formation are likely 
to be found much less frequently. Evaporation over 
land need by no means be small unless the land 
surface is very arid (desert); in fact, evaporation over 
a moist soil or a ground covered with vegetation may 
be comparable to, or even larger than, evaporation 
from a sea surface. A duct may therefore be formed 
when dry, warm air flows over a colder ground surface 
capable of evaporation. The temperature excess and 
humidity deficit may again be defined as above. 

Land and sea breezes often produce ducts near 
coastal regions. These winds are of thermal origin 
and are produced by temperature differences between 
land and sea. The mechanism is illustrated in Figure 
30. During the day, when the land gets warmer than 


WARM COLD 



LAND SEA 

SEA BREEZE 


COLD 




LAND SEA 

LAND BREEZE 


Figure 30. Land and sea breezes. 


the sea, the air rises over the land and descends over 
the sea and causes an air circulation in which the 
wind blows from sea to land (sea breeze) in the lowest 


levels. Vice versa, if during the night the land becomes 
colder than the sea, a circulation in the opposite 
direction arises. This is the land breeze. As a rule, 
this type of phenomenon is extremely shallow, and 
the winds do not extend above a few hundred feet 
at the most. Often there is a reverse wind in the 
layer above the land or sea breeze layer. A sea breeze 
may modify the advective conditions described above 
in various ways, and extremely strong ducts have 
been observed repeatedly under sea breeze condi¬ 
tions. The land and sea breezes are of a strictly local 
nature and in some cases will extend only a few 
kilometers to both sides of the shore. Nevertheless 
this region may be an important part of the trajec¬ 
tory of radiation. These breezes develop only under 
fairly calm conditions; under conditions of moder¬ 
ately strong wind, the sea and land breeze will be 
perceptible only as a slight modification of the 
existing wind. Because of their limited extent, fore¬ 
casting of these breezes requires a study of the local 
wind and temperature conditions. 

Advective ducts caused in the manner described 
here are often quite limited horizontally. This is 
especially true if a sea breeze is involved. The 
assumption made throughout this report, namely 
that the stratification of the air is of infinite extent 
horizontally, will no longer be valid, and superrefrac¬ 
tion may be restricted to a stretch along the coast. 

Ducts over the Open Ocean 

A type of duct that is somewhat similar to the 
advective duct described above is found over the 
open ocean where the air has had an extensive over¬ 
water trajectory. It has been studied in experiments 
carried out at the island of Antigua in the West 
Indies. The subsequent description refers to this 
particular location, but on the basis of experience 
gained operationally and in other experiments it may 
be presumed that similar conditions prevail in 
numerous other regions of the world, particularly in 
the trade wind regions. 

At Antigua, in winter and early spring when these 
tests were made, the wind is usually from the north¬ 
east since the island is situated at the southeastern 
fringe of the so-called Bermuda High, a large semi¬ 
permanent circulation system over the North 
Atlantic, extending from about 10° to 30° North 
latitude. The air at Antigua has thus had an ocean 
trajectory of thousands of miles. The relative hum¬ 
idity is of the order of 60 to 80 per cent, indicating 





RADIO METEOROLOGY 


215 


that in spite of the long passage over the sea no 
diffusion equilibrium has been established between 
the sea surface and the moisture in the lower atmos¬ 
phere. On the other hand, there is little difference 
between the air and sea temperature, the latter 
being rather constant at 25 C and the former varying 
between 23 and 26 C. The air is, therefore, nearly 
in convective thermal equilibrium with the sea sur¬ 
face, and no appreciably “dry” duct can develop. 
The duct is caused by the moisture variation in the 
lowest layers. 


200 


160 


120 


80 


40 


-r 

MIXED / 

"V 

1 

r 




n 

ii 





it 

i 





i ° 





iX 

i 

i _ 

5 


WATER 

SURFACE 


340 


350 


360 


370 


380 


3 SO 


M MODIFIED INDEX -► 

Figure 31. M curve over West Indian Ocean. 


A typical M curve is shown in Figure 31. It may 
be seen that at as small a height as 0.5 m above the 
sea M has a value much lower than at the surface 
itself. As the surface value of M is obtained by the 
assumption that the air in immediate contact with 
the water is saturated with moisture, this indicates 
that 0.5 m above the water the moisture content of 
the air is still appreciably below saturation. The 
moisture in the lowest levels is subject to consider¬ 
able variations caused partly by turbulence, partly 
by the waviness of the sea surface. M curves, such 
as Figure 31, are obtained by averaging over several 
measurements. 

These ducts are much lower than the advective 
ducts discussed in the previous section; their height 
is about 12 to 15 m (around 40 ft). The effective 
decrease of M in the duct (apart from the sharp 
decrease in the lowest half meter) is of the order 
of 4 to 8 MU. 


The latter figure depends somewhat on the wind 
speed. There is a maximum decrease of 8 MU at a 
wind speed of about 8 m per sec (13 miles per hour) 
and lower values for both lower and higher wind 
speed. The duct height in turn shows a very slight 
dependence on wind speed, increasing somewhat with 
increasing speed. 

These ducts are so low that they are not very 
effective for trapping of waves even as short as S 
band, presumably on account of strong leakage (see 
Section 17.2.6), and signal strength is not increased 
when an S-band transmitter or receiver is placed 
inside the duct. For K band, on the other hand, the 
trapping effect is marked; on raising the transmitter 
or receiver from the ground a maximum of signal 
strength is observed at about 9 m, but from there on 
the signal begins to decrease up to about 20 m (overall 
decrease 5 db); at greater heights the signal gradually 
rises again. 

These ducts appear to be a permanent feature at 
Antigua, at least during the season these observa¬ 
tions were carried on. This is probably true also for 
many locations in the trade wind belt. The daily 
variation of weather phenomena and of duct charac¬ 
teristics at such purely maritime locations seems to 
be insignificant. 

17 35 Nocturnal Cooling—Daily Variations 

A daily variation of surface temperature occurs 
only over land. During the day the heating is caused 
by the sun’s rays, and the cooling of the ground 
surface during the night is produced by radiation 
from the ground. The diurnal temperature variation 
of the sea is extremely small. However, shallow 
bodies of water sometimes have an appreciable 
diurnal variation. 

The radiation which causes nocturnal cooling of 
the ground is temperature or heat radiation which is 
composed of waves in the infrared portion of the 
spectrum. It is the same kind of radiation that is 
given off by a hot stove or electric heater, but since 
the temperature of the earth is less than that of a 
stove the earth emits comparatively less heat radia¬ 
tion. Nevertheless, radiation is a very powerful agent 
in cooling the ground. From about sunrise until the 
late afternoon, the surface of the earth gains more 
heat from the sun and atmosphere than it loses by 
radiation to space; in the late afternoon and during 
the night, the surface loses more heat than it gains. 
The amount of heat radiated is very nearly inde- 
















216 


TROPOSPHERIC PROPAGATION AND RADIO METEOROLOGY 


pendent of the physical constitution of the ground 
but is dependent upon its temperature and increases 
very rapidly with a rise in ground temperature. 

The atmosphere has a “blanketing” effect upon 
the infrared radiation emitted by the ground. The 
atmosphere itself absorbs and emits infrared radia¬ 
tion, and the cooling of the ground may be greatly 
reduced by the action of the atmosphere. The 
blanketing effect is least with a clear sky and dry, 
cool air; it is somewhat stronger when, with a clear 
sky, the atmosphere is very warm and humid, as in 
the tropics. A cloud will produce a distinct blanket¬ 
ing effect, and with a complete overcast of low cloud 
the blanketing is so pronounced that the nocturnal 
cooling of the ground is reduced to only a small 
fraction of its value with clear skies. 

The loss of heat from the ground is distributed by 
turbulence over the lowest layers of the atmosphere, 
thus giving rise to a temperature inversion. Inver¬ 
sions of this type are strongest in temperate and 
cold climates with a clear sky and cold, dry air 
overhead; they are less pronounced in the tropics 
with humid air and a clear sky and are practically 
absent with an overcast sky. A meteorologist, after 
some experience, can estimate the magnitude of an 
inversion to be expected with given local weather 
conditions. 

Temperature inversions, by themselves, can at 
best produce only weak ducts, but strong ducts may 
result when the inversion is accompanied by a suffi¬ 
cient moisture lapse. This requires that the air be 
dry enough to allow evaporation into it from the 
ground. In warmer climates where the transition 
between night and day is rapid, evaporation may 
set in in the early hours of the morning before the 
nocturnal inversion has been completely destroyed 
by the action of the sun. A strong duct will then be 
formed for a short period. This condition seems to 
be frequent during certain seasons in Florida. 

It is obvious that the shape of the M curve, when 
it deviates from the normal, may undergo rapid 
variations with the period of a day. One example 
has just been quoted; another is illustrated by the 
advective ducts over the North Sea produced by the 
mechanism described in Section 17.3.3. These ducts 
usually form in the hours before midnight and last 
until the early hours of the morning. 


Contrary to what might perhaps be expected, the 
formation of fog results, in general, in a decrease of 


refractive index. When fog forms, e.g., by nocturnal 
cooling of the ground, the total amount of water in 
the air remains substantially unchanged, but part 
of the water changes from the gaseous to the liquid 
state. The contribution of a given quantity of water 
to the refractive index is found to be far less when 
the water is contained in liquid drops than when it 
exists in the form of vapor. The formation of fog, 
therefore, results in a reduction of the amount of 
water vapor contributing to the value of M. If there 
is a temperature inversion in the fog layer, the 
saturation vapor pressure increases with height, and 
a substandard M curve frequently results (see Figure 
20, curve lb). This occurs with radiative fog (caused 
by nocturnal cooling of the ground) and also with 
advective fog (caused by the advection of warmer 
air over a cooler surface). Advective fog is very 
common in the Aleutian Islands and off Newfound¬ 
land. 

If fog causes a substandard M curve, it is to be 
inferred that the rays will be bent upward, instead 
of downward as with superrefraction, and lead to a 
weakening of the field in the lowest layers, even to 
the point of producing a complete fade-out of radio 
reception. Appreciable reduction of radar ranges and 
interruption of microwave transmission have 
frequently been observed in such cases. 

Fog, however, does not always produce a sub¬ 
standard M curve, though this is the most common 
case. In certain other less frequent types of fog, the 
temperature (and thereby the vapor pressure) may 
be constant or increase with height through the fog 
layer. In this event near-standard propagation will 
prevail, or a duct may develop when the temperature 
inversion is strong enough. An example is steam fog, 
formed when cold air passes over a warm sea (see 
also Section 17.3.9). 

Subsidence—Dynamic Effects 

The temperature inversions discussed so far owe 
their existence to the modification of air by contact 
with the ground, but subsidence inversions are 
produced by a mechanism of an entirely different 
nature. By subsidence is meant the sinking of air, 
that is, a vertical displacement, which must of course 
be accompanied by a lateral spreading (divergence) 
in the lower part of the subsiding column of air; 
otherwise there would be an accumulation of air in 
the lower levels. The thermodynamic analysis of this 
complex process shows that if the effect of subsidence 



RADIO METEOROLOGY 


217 


is strong enough a temperature inversion will be 
created. Since this process does not require the 
presence of a ground surface, it may occur, and in 
fact often does occur, aloft in the atmosphere. The 
effects of subsidence frequently are the most pro¬ 
nounced at an elevation of the order of a kilometer 
or more. 

As a general rule, subsidence occurs in regions of 
high barometric pressure. In fact, subsidence always 
does occur in such regions, but it may not always be 
intense enough to give rise to a strong temperature 
inversion. The flow of air in a barometric High is 
shown in Figure 32 as it appears on a weather map 


ILLUSTRATING SUBSIDENCE (SINKING) IN HIGH PRESSURE AREA 



Figure 32. Characteristics of subsidence. 


in horizontal projection, and also in a vertical cross 
section. 

With subsidence, the air as a rule is very dry, and 
there is nothing in the process which can change the 
moisture content or produce moisture gradients. If, 
however, the dry air finds itself over a surface capable 
of evaporation, such as the sea surface, a steep 
moisture gradient may be established and a duct 
will be created. It is thus seen that subsidence in 
itself does not produce a duct, except in extreme 
cases, but it can act as an auxiliary factor and greatly 
enhance the formation of a duct whenever other 
conditions are favorable. Thus, forecasts of super- 
refraction based on a purely advective mechanism, 
or purely on radiative cooling or evaporation, may 
have to be modified in the presence of subsidence; 
an otherwise very weak duct may be converted into 
a strong duct by the effect of subsidence upon the 
lower strata. 

Strong subsidence effects are of frequent occur¬ 
rence on the southern California coast where they 
may continue with little change for days at a time. 


At times the duct is elevated, giving an elevated 
S-shaped M curve like Ilia in Figure 20. Again the 
duct may extend practically from the ground up 
with M curves similar to curves II or Illb in Figure 
20. The elevation of the top of the duct may vary 
from 300 to 5,000 ft, and the thickness may lie 
between a few feet and 1,000 ft. Coverage diagrams 
and the corresponding M curves for several typical 
situations are illustrated in Figure 24. 

For a number of reasons the meteorological condi¬ 
tions in a barometric High are favorable for the 
formation of ducts. Among the favorable factors 
are: subsidence, creating very dry air into which 
evaporation from the surface can take place; again 
subsidence, creating temperature inversions; calm 
conditions preventing mixing of the lowest layers by 
frictional turbulence and maintaining the thermal 
stratification caused by radiative cooling or local 
breezes; clear skies producing nocturnal cooling 
over land. 

The conditions in a barometric Low, on the other 
hand, generally favor standard propagation. A lifting 
of the air, the opposite of subsidence, usually occurs 
in such regions and is accompanied by strong winds. 
The combined effect is to destroy any local thermal 
stratification and to create a deep layer of frictional 
turbulence. The air is therefore well mixed, and 
nonstandard vertical temperature and moisture 
gradients are wiped out in the early stages of their 
creation. Moreover, the sky is usually overcast in a 
low-pressure area and nocturnal cooling, therefore, 
is negligible. 

To summarize, high-pressure regions, clear skies, 
and calm air are conducive to duct formation, while 
low-pressure areas, cloudy skies, and winds favor 
standard refraction. 

Fronts in the atmosphere are possible sources of 
refractive effects. A front is a surface of discontinuity 
which separates two air masses of different tempera¬ 
tures. The surface slants at an angle of 1° to 2° with 
the horizontal, with the colder air forming a wedge 
under the warmer air. Fronts are a common occur¬ 
rence in the atmosphere, and it might be thought 
that they should have a considerable influence on 
wave propagation. This is, however, not borne out 
by English radar experience, which shows very little 
superrefraction connected with fronts. The explana¬ 
tion is probably that fronts are invariably accom¬ 
panied by low-pressure areas, and turbulence along 
a front is usually so strong that the transition from 
the cold air to the overlying warm air takes place 







218 


TROPOSPHERIC PROPAGATION AND RADIO METEOROLOGY 


continuously over a vertical distance of about a 
kilometer. Propagation conditions might, however, 
be somewhat different with fronts in sub-tropical 
climates, although our knowledge is still inadequate 
on this point. In one-way transmission frontal effects 
have been studied to a limited extent (see Section 
17.3.9). 

Seasonal and Global Aspects 
of Superrefraction 

Although the general picture is still incomplete, 
enough is now known about the geographical and 
seasonal aspects of superrefraction to warrant a 
general summary. 

Atlantic Coast of the United States- 

Along the northern part of this coast superrefrac¬ 
tion is common in summer, while in the Florida 
region the seasonal trend is the reverse, with a 
maximum in the winter season. 

Western Europe 

On the eastern side of the Atlantic, around the 
British Isles and in the North Sea, there is a pro¬ 
nounced maximum in the summer months. Conditions 
in the Irish Sea, the Channel, and East Anglia have 
been studied by observing the appearance or non- 
appearance of fixed echoes (see Figure 33). Additional 



Figure 33. Diurnal frequency of long-range fixed echoes 
at North Foreland, Kent. Wavelength 10 cm. 


data based on one-way communication confirmed the 
radar investigations. 

Mediterranean Region 

The campaign in this region provided good oppor¬ 
tunities for the study of local propagation conditions. 
The seasonal variation is very marked, with super- 
refraction more or less the rule in summer, while 


conditions are approximately standard in the winter. 
An illuminating example is provided by observations 
from Malta, where the island of Pantelleria was 
visible 90 per cent of the time during the summer 
months, although it lies beyond the normal radio 
range. 

Superrefraction in the central Mediterranean area 
is caused by flow of warm, dry air from the south 
(sirocco) which moves across the ocean and thus 
provides an excellent opportunity for the formation 
of ducts. In the winter time, however, the climate in 
the central Mediterranean is more or less a reflection 
of Atlantic conditions and hence is not favorable for 
duct formation. 

The Arabian Sea 

Observations covering a considerable period are 
available from stations in India, the inlet to the 
Persian Gulf, and the Gulf of Aden. The dominating 
meteorological factor in this region is the southwest 
monsoon that blows from early June to mid-September 
and covers the whole Arabian Sea with moist equa¬ 
torial air up to considerable heights. Where this 
meteorological situation is fully developed, no occur¬ 
rence of superrefraction is to be expected. In accord¬ 
ance with this expectation the stations along the 
west side of the Deccan all report normal conditions 
during the wet season (middle of June to middle of 
September). During the dry season, on the other 
hand, conditions are very different. Superrefraction 
then is the rule rather than the exception, and on 
some occasions very long ranges, up to 1,500 miles 
(Oman, Somaliland), have been observed on 200-mc 
radar on fixed echoes. 

When the southwest monsoon sets in early in 
June, superrefraction disappears on the Indian side 
of the Arabian Sea. However, along the western 
coasts conditions favoring superrefraction may still 
linger. This has been reported from the Gulf of Aden 
and the Strait of Hormuz, both of which lie on the 
outskirts of the main region dominated by the 
monsoon. The Strait of Hormuz is particularly inter¬ 
esting as the monsoon there has to contest against 
the shamal from the north. The Strait itself falls at 
the boundary between the two wind systems, forming 
a front, with the dry and warm shamal on top, and 
the colder, humid monsoon underneath. As a conse¬ 
quence, conditions are favorable for the formation of 
an extensive radio duct, which is of great importance 
for radar operation in the Strait. 










RADIO METEOROLOGY 


219 


The Bay of Bengal 

Such reports as are available from this region 
indicate that the seasonal trend is the same as in 
the Arabian Sea, with normal conditions occurring 
during the season of the southwest monsoon, while 
superrefraction is found during the dry season. It 
appears, however, that superrefraction is much less 
pronounced than on the northwest side of the 
peninsula. 

The Pacific Ocean 

This region appears to be the one where, up to 
the present, least precise knowledge is available. 
There seems, however, to be definite evidence for the 
frequent occurrence of superrefraction at some loca¬ 
tions; e.g., Guadalcanal, the east coast of Australia, 
around New Guinea, and on Saipan. Along the 
Pacific coast of the United States observations indi¬ 
cate frequent occurrence of superrefraction, but no 
statement as to its seasonal trend seems to be 
available. The same holds good for the region near 
Australia. 

In the tropics there is found a very strong and 
persistent seasonal temperature inversion, the so- 
called trade wind inversion. It has no doubt a very 
profound influence on the operation of radar and 
short-wave communication equipment in the Pacific 
theater. 

17 39 Fluctuations in Signal Strength 
with Time 

A number of different causes tend to produce 
variations of signal strength with time. These are 
discussed briefly in the following paragraphs. 

Target Modulation 

Very rapid fluctuations having periods of only a 
small fraction of a second frequently are encountered 
in radar observations, especially with centimeter 
waves. These fluctuations arise as a consequence of 
the internal motions of the target and are especially 
noticeable for aircraft. Similar effects have been 
observed with reflection of microwaves from wooded 
hills, the fluctuations in signal probably being caused 
by foliage moving in the wind. 

Effect of Waves on the Sea 

A similar phenomenon is observed when the trans¬ 
mitter and receiver are so situated that reflection 


from a water surface contributes to the received 
signal strength. Owing to irregularities of the water 
surface and their rapid change with time, variations 
in signal strength will appear. The fluctuations 
arising in this way have a time scale of the order of 
a second, in the case of a lightly ruffled sea (see 
Figure 34). Evidently rays reflected from different 


t- 1 - 1 - 1 - 1 - 1 -r 



_I_l-1-1_I-1-1-1-L 

01234 56789 

SECONDS 


Figure 34. Variation in signal strength with time in 
radiation reflected from the sea (direct radiation cut off). 

X = 9 cm. 

parts of the water surface interfere, and with the 
changing form of the surface the interference pattern 
at the place of the receiver changes accordingly. The 
time scale of these changes must be connected with 
the speed, wavelength, and amplitude of the waves, 
but the exact relation is not known thus far. 

Tidal Effects 

The rise and fall of the tide produces a gradual 
variation in signal strength by changing the inter¬ 
ference between the direct and the reflected rays. 
The path difference between these rays is 2hih2/R, 
where hi, h 2 are the heights of the transmitter and 
receiver relative to the instantaneous water level and 
R is the range. The corresponding difference in phase 
between the two rays is equal to 


measured in radians. The variation in the signal 
strength depends upon the variation in 0. It is small 
when the change in <t> is small and increases to a 
maximum for a change in <f> of tt radians. It follows 
from equation (26) that the tidal effect increases 
with the variation in the water level of the tide and 
with the heights hi and hz and decreases with the 
range and the wavelength. 

Scintillations 

The really conspicuous fluctuations in propagation 
conditions, however, are due to changing meteoro¬ 
logical conditions. A characteristic type is an irregular 
fluctuation in signal strength on a time scale of the 
order of a minute and with an amplitude rarely 






220 


TROPOSPHERIC PROPAGATION AND RADIO METEOROLOGY 


exceeding 2 db. It varies in intensity according to 
the state of turbulence in the air along the propaga¬ 
tion path. In perfectly calm air the fluctuation is 
practically nonexistent but becomes quite noticeable 
in turbulent air. This sort of fading is analogous to 
the scintillation of the fixed stars or the unsteadiness 
of the telescopic picture of distant objects occurring 
especially on warm summer days. The physical 
explanation for the scintillations is found in the 
fact that the turbulent motion of the air produces 
irregular variations in refractive index. The conse¬ 
quent irregular bending of rays passing through such 
a medium produces a patchy distribution of intensity 
over the wave front. In the case of stellar scintilla¬ 
tions the main change in refractive index is caused 
by fluctuations in air density, and the significant 
•level of turbulence is at an elevation of several 
thousand feet. For radio waves fluctuations of water 
vapor density are the chief cause of the scintillations, 
and the active region is consequently close to the 
ground. For typical radio scintillations see Figure 
35A. 



A STEADY SIGNAL AVERAGE LEVEL 


h, * 125 FT h 2 = 50 FT 



B HIGH AVERAGE SIGNAL WITH DEEP FADING 
h 1 = 125 FT h 2 = 25 FT 


5 

o 

i 

UJ 

CD 

CD 

O 


»- 

►— 

< 


o 

_l 

UJ 

CD 


CD 

O 



£ 

o 

-I 

UJ 

CD 

CD 

O 


Figure 35. Signal strengths for X = 10 cm over sea. 


Duct Fades 

A duct is normally accompanied by fades in the 
signal strength of large amplitude (up to 30 db) and 
of moderate periods (of the order of 15 min). A 
detailed theory of this type of fluctuation in signal 
strength is not available. When the duct is fully 
developed, there is a large-scale deviation from 
standard conditions with regard to mean field 
strength. If, in particular, both transmitter and 
receiver are situated inside the duct, there is a great 
increase in received field strength. Suppose, however, 
that for some reason the duct does not function 
according to the simple theory. The field strength at 
the receiver may then drop to the value correspond¬ 
ing to standard conditions. The observed fades 
exhibit just this characteristic in that they consist 
in sharp drops of signal strength down from a mean 
upper level. The conditions are illustrated in Figure 
35, which shows three records obtained for a 22-mile 
path over sea. Figure 35A shows the normal record 
on a calm day when the only disturbances are due 
to scintillations. The record shown in Figure 35B, 
on the other hand, was obtained for a condition of 
simple surface trapping, with transmitter and receiver 
inside the duct. It will be noted that the signal 
strength is considerably above the 95-db average as 
given in Figure 35A. 

Duct-type fades have been observed over land as 
well as over sea and appear to form a characteristic 
feature from which the presence of superrefraction 
may be inferred. 

Blackout 

Figure 35C shows a fade in which the signal level 
is far below average and which for this reason is 
called “blackout.” This type is liable to occur when 
warm, moist air is cooled from below (see the sub¬ 
standard M curve lb in Figure 20) and is often 
correlated with fog. The main irregularities in signal 
strength are again on a time scale of the order of 34 
hour; the amplitude of variation is smaller than in 
the preceding case and rarely exceeds 10 db. 

Fronts and Thunderstorms 

On several occasions marked variations in signal 
strength have been observed when fronts pass 
between the transmitter and receiver. The passage 
of the front itself is marked by very rapid and deep 
fluctuations, followed by less violent changes on a 






























































RADIO METEOROLOGY 


221 


longer time scale (see Figure 36). It appears that 
similar effects are likely to occur during thunder¬ 
storms. 



TIME GMT 


Figure 36. Effect of a front on signal strength (Hasle- 
mere-Wembley Link, England). 

Fog 

Some peculiar effects were observed by transmission 
through fog over an experimental overland radio link 
in England. The effect of a shallow layer of radiation 
fog in the early autumn (September-October) was 
to produce a nearly complete fade-out of signal 
strength which lasted for hours and rose to normal 
as the fog cleared. The explanation of this effect is 
probably the same as in the case of the “blackout” 
type fades discussed above, indicating that radiation 


fog produces a substandard M curve. Later in the 
autumn (November-December) or winter (January) 
it was found that the effect of fog was quite different. 
In this season the signal strength was increased and 
deep fades appeared which are reminiscent of the 
duct-type fades described earlier. 

Fading on Different Wavelengths 

Several experiments have been performed in which 
transmitters working on different wavelengths oper¬ 
ate simultaneously over the same path and the 
received field intensities are recorded on the same 
chart. Figure 37 shows one such record for the 42.5- 
mile (optical) path from the Empire State Building, 
New York City, to Hauppauge, Long Island, for 
May 14 and 15, 1943, at frequencies of 474 me and 
2,800 me. It will be noticed that on May 14 up to 
about 5:45 p.m. the two records show a close 
agreement. At 6:00 p.m. violent fading sets in on 
both frequencies, but with great diversity in detail. 
Not infrequently the signal on one frequency increases 
while on the other frequency it decreases. About 1:00 
a.m. on May 16 the disturbance dies down, and the 
initial harmony in the two records is restored. 



Figure 37. Simultaneous variations of signal strength with frequency. (Empire State Bldg, to Hauppauge, L. I., N. Y.) 























































































































222 


TROPOSPHERIC PROPAGATION AND RADIO METEOROLOGY 


Experiments over the longer (nonoptical) path 
from the Empire State Building, New York City, to 
Riverhead, Long Island (range 70.1 miles), showed 
much greater diversity in the fading patterns for the 
different frequencies. On the other hand, observa¬ 
tions over the British radio link from Guernsey to 
Chaldon on 60 me and 37.5 me (range 85 miles) 
showed that if there were marked variations on one 
frequency similar results were likely to be found on 
the other frequency. 

Reliability of Circuits 

The reader must be warned that the amount of 
the fading in the signal strength is not a measure of 
the performance of radar and communication circuits. 
These will operate successfully so long as the periods 
of low signal are relatively short. Neither the scin¬ 
tillations of Figure 35A nor the larger dips of Figure 
35B would seriously affect operation, but a prolonged 
signal such as in Figure 35C would certainly interfere 
seriously with communication and radar performance. 

Some quantitative data are available from the 
transmission path referred to in the previous para¬ 
graph. On the optical path, New York to Hauppauge, 
the range of signal fluctuations increased rapidly with 
increasing frequency. On 45 me the “undisturbed” 
level (the observational equivalent of standard) was 
21 db below free space with an amplitude of fluctua¬ 
tions that very rarely exceeded + 4 db. On the 474- 
mc circuit the undisturbed level was 3.5 db below 
free space while the fluctuations varied between 10.5 
db above to more than 30 db below free space. The 
level was 5 db or more below the undisturbed value 
during 0.01 per cent of the time in January and 
during 0.4 per cent of the time in July. On the 2,800- 
mc circuit the undisturbed level was — 2 db below 
free space; the maximum was 12 db above and the 
minimum more than 25 db below free space. During 
0.15 per cent of the time the signal was 5 db or more 
below the undisturbed level in January; the corre¬ 
sponding figure for July was 3.6 per cent. The conclu¬ 
sion may be drawn from this and similar experiments 
that over optical paths transmission becomes gradu¬ 
ally less reliable as the frequency is raised. 

Over the nonoptical path, New York to Riverhead, 
the margin of fluctuations was much larger. On the 
45-mc circuit the undisturbed value was 35 db below 
free space, the maximum 18 db below, and the 
minimum more than 50 db below free space. During 
1.6 per cent of the time the signal was 5 db or more 


below the undisturbed level. On the 474-mc circuit 
the undisturbed signal was 30 to 35 db below free 
space, the maximum 10 db above, and the minimum 
44 db below free space. During 0.47 per cent of the 
time the signal was 5 db or more below the undis¬ 
turbed value. At 2,800 me the undisturbed signal 
was 50 to 60 db below free space near the limit of 
sensitivity; the observed maximum was 13 db above 
free space, and the minimum could not be observed. 
In this case the effects of superrefraction were quite 
pronounced. In January the signal was less than 40 
db below free space during 6.5 per cent of the time; 
the corresponding figure for July is as high as 33 
per cent. 

The reliability of these transmission circuits is 
shown in Figure 38. Here, both for the optical and 
nonoptical paths, the percentage of time during 
which the signal strength was below specified values 
is plotted for the various frequencies used. The 
specified values of signal strength, for each frequency 
and path, are measured relative to the corresponding 
undisturbed value. The results, which give averages 
of the performance during July 1943 and January 
1944, indicate that the reliability increases appreci¬ 
ably with decreasing frequency. 

It must be said that the New York area where 
these experiments were made is not particularly 
affected by blackout situations, and the results are 
probably not typical for locations where blackouts 
are a frequent occurrence. The general nature of 
these data is confirmed by results of extensive 
experiments in England and in Massachusetts Bay. 

Scattering and Absorption 
by Water Drops 

As microwave sets have come into general use in 
recent years the “rain echoes” frequently seen on 
the scope have attracted attention. The possibility 
of using microwave radar as an aid to meteorological 
forecasting and for aerial navigation was early recog¬ 
nized and is now being put to operational use. 

At first sight, ground clutter resulting from trap¬ 
ping of radiation in a ground-based duct and rain 
reflections look somewhat alike on the scope of a 
radar set. At closer inspection differences appear; 
the cloud pictures are usually more fuzzy and less 
sharply defined than the echoes received from ground 
targets. An experienced operator usually has little 
difficulty in distinguishing rain echoes from echoes 
of targets or objects at the ground, but occasional 



RADIO METEOROLOGY 


223 



Figure 38. Reliability of circuit. Average of July 1943 and January 1944. (Empire State Building to Hauppauge and 
Riverhead, L. I., N. Y.) 


mistakes have been reported, especially from the shows that the amount of scattering increases very 
tropics. rapidly as the wavelength is decreased. It also 

Rain echoes are a result of the scattering of micro- increases rapidly with increasing drop diameter. On 
waves by the raindrops. Electromagnetic theory account of this sharp variation the scattering effects 





















































































































224 


TROPOSPHERIC PROPAGATION AND RADIO METEOROLOGY 


become appreciable only when the wavelength is 
below a certain maximum value and when the drops 
exceed a certain critical size. Rain echoes are rarely 
observed at longer waves than S band, but they are 
common at S band and become very important at 
the shorter microwaves. 

For a time it was thought that clouds could 
produce microwave echoes, but more thorough inves¬ 
tigations have now established the’fact that the 
droplets in clouds are too small to produce appreci¬ 
able scattering. Only drops that are large enough to 
constitute genuine rain are seen by a radar, and, 
especially at S band, light rains will often escape 
detection. The term “storm echo,” invented at a 
time when the origin of these echoes was not yet 
clearly understood, should be avoided, and the terms 
“rain echo” or “precipitation echo” should be used 
instead. A rain seen by the radar is not necessarily 
recorded by an observer at the ground, as the rain 
may be confined to the free atmosphere and never 
reach the earth. This occurs either when the rain 
falls in an ascending stratum of air where the air 
rises more rapidly than the drops fall or when the 
raindrops evaporate again before reaching the 
ground. Both cases occur quite commonly in the 
atmosphere, especially under convective conditions 
such as are indicated by cumulus clouds and thunder¬ 
storms. Snow may also be seen on microwave scopes 
provided the snowfall is sufficiently heavy. 

While clouds themselves do not produce microwave 
echoes, they may contain falling rain of one of the 
forms just indicated. Visual appearances are deceiv¬ 
ing, and an imposing looking cumulus cloud might be 
entirely invisible on the scope, whereas a cloud that 
is inconspicuous to the eye but contains falling 
raindrops might give a pronounced echo. 

The question of “shadow” cast by a storm echo 
is of some operational interest. A shadow is formed 
when the absorption that accompanies scattering by 
the raindrops becomes so strong that the remaining 
radiation no longer suffices to produce visible echoes 
from targets behind the rain area. This effect is 
pronounced on X band, and even more on K band, 
and is often quite conspicuous with airborne equip¬ 
ment where it may happen that a rain storm blanks 
out a sector of the sweep. On S band the absorption 
is usually much weaker and targets can often be seen 
behind a rain echo. 

The usefulness of rain echoes for aerial navigation, 
particularly in the tropics, is now so generally known 
that the subject need not be discussed further. 


174 SNELL’S LAW 

The ordinary law of refraction known as Snell's 
law may be expressed as 

no sin ft = sin ft , 

where ft and ft are the angles which the ray makes 
with the perpendicular to the boundary. Here it is 
more convenient to take the angle a between the 
ray and the boundary surface. Snell’s law then reads 


Uq COS do — W-i COS Oil . 

The refraction at a sharp boundary is shown in 


Figure 39A. 

If there are 

several 

boundaries it is 



n 3 


"1 

A 

n 2 

Az 

3^ 

0 

c 

BOUNDARY 

"i 

A 

/ 


n o <*c 

f 1 - 


n 2 



Figure 39. Application of Snell’s law of refraction. 

readily seen that Snell’s law generalizes (Figure 
39B) to 

no cos ao = Wi cos a.i — ^2 cos 0:2 = * * ' , 
and for a continuously variable layer it becomes 
n cos a — no cos ao , 

where n and a are continuous variables which are 
functions of the height and the index 0 designates an 
arbitrary reference level. 

Snell’s law for a curved earth may be derived from 
Figure 39C. For successive boundaries it is found: 











snell’s law 


225 


no sin ft, = Wi sin /3' 0 , 
rii sin ft = n 2 sin fi'i , etc. 

Multiply the first equation by r 0 , the second by n, 
etc. Then 

n 0 r 0 sin /3 0 = Wo sin /3' 0 , 
uiTi sin ft = n 2 ri sin /S'i, etc. 

But from the triangle OAB 

sin ft 0 _ sin ft 

, etc. , 


n 0 r 0 sin ft = sin ft = n 2 r 2 sin ft = • • • . 

Again introducing the angle o: with the horizontal 
and making the transition to a continuously variable 
refractive index gives 

nr cos a = n 0 r 0 cos a 0 , 

which is the generalization of SnelPs law for a curved 
earth. r 0 may be chosen as any convenient height, 
say a for the surface of the earth or a + hi for the 
height of the transmitter, and n 0 is the corresponding 
value of n. 


so that: 





Chapter 18 

THEORETICAL TREATMENT OF NONSTANDARD 
PROPAGATION IN THE DIFFRACTION ZONE* 


T he assumptions and restrictions underlying this 
presentation are: 

1. We concern ourselves with problems of the 
diffraction region only: the field is calculated at 
considerable distance from the transmitter and not 
too great height above the ground. 

2. The plane-earth model is used, in which the 
( effect of curvature is simulated by using the modified 
index M instead of the index of refraction n. 

3. The earth’s surface is assumed smooth, and M 
depends on height only (horizontal stratification). 

4. Simplified boundary conditions at the earth’s 
surface are used, appropriate to the treatment of the 
diffraction zone at microwave frequencies. This 
results in a formula which refers only to a discrete 
spectrum of modes and makes the calculations 
independent of polarization. 

5. The directional pattern of the transmitter need 
not be considered, since only the intensity at the 
azimuth in question and within 1 degree of the hori¬ 
zontal plane is of importance. The problem solved 
is that of a vertical dipole, electric or magnetic. 

6. The field is described in terms of a single 
quantity \F, the Hertzian vector being (0,0,40. Then, 
at a point in the diffraction region, 

actual field strength = | SF | 2 • d 2 • E 0 , (1) 

with d = horizontal distance from source, 

E o = free space field at distance d. 

An expression for 'F can then be found in the form 

'Krf.z) = 2] e ~ yJ O.(*0 U m {z) , (2) 

m 

where hi = transmitter height; 

z = height at which 4> is calculated; 

2tt 

co = 2tJ, k = — . 

y m and U m are characteristic values and functions 
of the boundary value problem 

~ + [km\z) + t 2 ] v = o, (3) 

a By W. H. Furry, Radiation Laboratory, MIT. 


, f Ue iut wave moving upward, z —> co , (4) 
wnere _ 0 ( 5 ) 

The modified index of refraction M is supposed to 
be defined without the factor 10 6 usually included. 

The functions U must be normalized in a suitable 
way. If we had not agreed to use simplified boundary 
conditions, the last equation (5) would be more 
complicated and would depend on the type of polari¬ 
zation. Also an integral would appear in addition 
to the discrete sum in the expression for 4>. The 
actual value for T, for the diffraction zone and 
microwave frequencies, would not be affected sig¬ 
nificantly. 

The quantities y m are complex: 

ym ~ *T ifim • (6) 

a m and are positive real quantities. It is convenient 
to think of the terms of the series as arranged in 
order of increasing a: 

0.1 < Q!2 < CX3 < ol \ * • * . 

These quantities determine the horizontal attenuations 
of the various modes. For large d only one or at most 
a few terms of the series are required to give the 
value of T. The quantities (3 m are all very nearly 
equal to k. The slight differences between the /3 m ’s 
determine the phase relations and hence the inter¬ 
ferences between the various modes. 

It is convenient to classify the modes into two 
types: (1) “Gamow” modes which are strongly 
trapped, so that a is very small; (2) “Eckersley” 
modes which are incompletely trapped or untrapped. 
The names “Gamow” and “Eckersley” refer to the 
men who devised the approximate phase integral 
methods which apply in the two sorts of cases. For 
practical purposes, when working within the diffrac¬ 
tion region, we need consider only the Gamow modes, 
or at most the Gamow modes and the first Eckersley 
mode. 

In order to be able to use the formula to calculate 
'F for a given index curve M(z), we must obtain the 
following information about the modes which are 
to be used: 

1. The characteristic values. 

2. “Raw” or unnormalized characteristic func- 


226 



NONSTANDARD PROPAGATION IN THE DIFFRACTION ZONE 


227 


tions, which satisfy the differential equation and the 
boundary conditions but still require multiplication 
by suitable normalization factors. 

3. The normalization factors. 

There are three methods of attack on the problem: 

1. Numerical integration of the differential equa¬ 
tion, accomplished in practice by the use of a 
differential analyser. 

2. Phase integral methods. 

3. Use of known functions and tables, for suitably 
chosen M curves. 

The method of numerical integration is being used 
intensively in England by Booker, Hartree, and 
others. It encounters considerable difficulties in con¬ 
nection with the fitting of the boundary condition 
at z —^ oo and also in the determination of normali¬ 
zation factors. These difficulties have been overcome 
by special and fairly elaborate procedures. In this 
country the feeling has been that we should direct 
our efforts toward the use of the other methods. 

If either method (2) or method (3) is to be readily 
applied to a variety of cases without a prohibitive 
amount of labor, the M curves must have a suitable 
form. The form indicated turns out to be the same 
in both cases. It consists of portions, each of which 
is a straight line. If enough such portions are used, 
any actual M curve can be accurately represented, 
but it is impractical to use more than a very few. 
Present efforts are directed toward dealing with 
cases where there are just two straight-line portions 
and there is no prospect of going beyond the cases 
with three (Figure 1). 



Figure 1. Schematic straight-line M curves. 


At first sight these curves look overly artificial, 
but there are considerations which indicate that 
they are really an altogether reasonable choice. First, 
some actually occurring curves have very much this 
sort of appearance. Second, the sharp breaks in the 
curves have no really strong effect on the results. 
Third, practical considerations severely limit the 
number of parameters which can be used in specify¬ 
ing the curve, so that a meticulous reproduction of 
every actual curve is out of the question. Fourth, 


the assumption of horizontal stratification is usually 
not well enough justified to make highly precise 
results really significant. 

The use of the jointed-line model for phase integral 
work was decided on last winter in the Radiation 
Laboratory . b 

The phase integral methods were pushed first, 
because the calculations are quite easy and do not 
require special tables of functions. Unfortunately 
the gaps between the regions of validity of the 
different phase integral approximations turn out to 
be extremely wide and to cover just the more inter¬ 
esting ranges of slope and duct height. This makes 
it necessary to resort to the exact solutions to deter¬ 
mine characteristic values and normalization factors. 
The phase integral methods provide limiting cases 
which can help in guiding the exact computations. 
Also the phase integral formulas are usually quite 
adequate for the computation of the “raw” charac¬ 
teristic functions, once the characteristic values are 
known. 

In order to make the exact calculation, we need 
tables for complex arguments of the solutions of the 
equation 


These solutions can be expressed in terms of the 
Airy integrals, but for greater convenience the solu¬ 
tions have been standardized in the form 

hj(z) = (!)' 2* H l(P) O'=1,2). 

The tabulation of these functions for | z \ < 6, on 
a square mesh 0.1 unit on a side is being done on the 
automatic sequence-controlled calculating machine 
at Harvard University. Work was begun in the latter 
part of August 1944, under authorization from the 
Bureau of Ships. Photostats of about one-fourth of 
the tables were obtained by November 1944. 

The present objective is to produce charts from 
which ai and ft and the normalization factor for the 
first mode can be obtained for any M curve made up 
of two straight portions, the upper one being of 
standard slope. After this, similar charts for the 
second mode, and perhaps the third and fourth, will 
be undertaken. When this has been done, the 
approximate determination of field strengths and 
coverage will be possible by a definite routine 
procedure. 

b The use of the solutions for this case in terms of Hankel 
functions was suggested by Lt. Comdr. Menzel. 






Chapter 19 

CHARACTERISTIC VALUES FOR THE FIRST MODE 
FOR THE BILINEAR M CURVE a 


T he model of an M curve composed of straight- 
line segments suggested itself to workers at the 
Radiation Laboratory early in 1944 as one in which 
phase integral calculations could be carried out very 
rapidly. At about the same time Lt. Comdr. Menzel 
suggested the use of this model together with tables 
of Hankel functions to obtain exact solutions. In the 
fall of 1944 it became evident that phase integral 
methods were not of much use with this model. 
Tables of the required Hankel functions, essentially 
standard height-gain functions, for complex argu¬ 
ment were prepared at the Harvard Computation 
Laboratory, and considerable effort was directed to 
the obtaining of exact solutions. 

Work at the Radiation Laboratory has been largely 
confined to the first mode for a curve composed of 
two segments. This work has progressed largely 
through the efforts of Miss Dodson and Miss Gill 
and Howard and Parker. Dr. Pekeris of the Columbia 
University Wave Propagation Group has been di¬ 
recting work on the second mode. 

The units, notation, and model are given by the 
following formulas and illustrated in Figure 1. 



Figure 1. Models and units. 


h = 


with 


■ ® • (*)• 
H (feet) = 7.24 [X(cm)]* , 

mtf 


L = 2 (jfcg 2 )-* = 2 


with L(thousand yds) = 6.69 [X(cm)]* , 

h d d 2 U . ,-wt . T j „ 

H ’ L ’Hii* + + U = 0 


a By W. H. Furry, Radiation Laboratory, MIT. 


The natural units of height and distance represent 
two different compromises between wavelength X 
and earth radius a, so that X -£■ H -f- L -*■ a form, 
very roughly, a geometric progression. It is seen that 
for microwaves, heights and distances occurring in 
practice are fairly small numbers of natural units. 

The M curves are plotted in terms of the height z 
in natural units and of a quantity Y which is simply 
M multiplied by a suitable wavelength dependent 
factor. The standard part of the curve then has 
slope unity. In the bilinear model the anomaly 
consists of a segment with slope s 3 times standard, 
or, in these diagrams, simply slope s 3 . For negative s 
there is a duct; s positive but less than 1 gives transi¬ 
tional cases; and s greater than 1 gives substandard 
cases. 

The essential quantity SF used in calculating the 
field is given by: 

x~* X 

m 

The power density is equal to the free space power 
density multiplied by ^ 2 d 2 . The characteristic values 
are complex: D = B + iA. For the standard case: 
Di = —1.17 + 2.02L (For X = 10 cm this corre¬ 
sponds to an attenuation of 1.22 db per thousand 
yards.) T consists of three factors: one, that for a 
plane wave, which can ordinarily be omitted; the 
second, a constant factor which depends on wave¬ 
length through L, the natural unit of distance [this 
factor can be replaced by just 2\/t if x 2 (= d 2 /L 2 ) 
instead of d 2 is written in the first line]; and finally 
the critical factor written in terms of natural units 
only and involving characteristic values and charac¬ 
teristic functions. The imaginary parts of the charac¬ 
teristic values are the coefficients of horizontal 
attenuation, and the characteristic functions are the 
height-gain functions. 

It is seen that for a typical microwave frequency 
the horizontal attenuation of the first standard mode 
(g = 0) is rather sizable. The plot of the height-gain 
curve shows that if both transmitter and receiver 
are at about 200 ft there is a gain of 50 to 60 db. 


\F = (e 


iut-2-iri dlX-iir/4 \ 2\/x 


228 








CHARACTERISTIC VALUES FOR THE BILINEAR M CURVE 


229 



Figure 2. First standard and first trapped mode. 


In discussing the behavior of U in relation to the 
Y curve, it is best to plot U or | U | rather than 
decibels. It is also helpful to draw a vertical line at 
the abscissa —B, and this is then usually used as 
the axis in plotting U or | U |. The diagram for a 
trapped mode shows that | U | shows exponential 
decay in the “barrier” region where the Y curve lies 
to the left of the line at —B. Below the barrier U 
shows oscillatory behavior, but with no nodes for 
the first mode; above the barrier U is a spiral, which 
shows only as a slow increase in the plot of | U |. 

This same difference in the behavior of U for Y > 


or < —B is a useful thing to remember in more 
general cases. Sometimes it is not quite so clear-cut 
as in this case of trapping. If A is not small, the 
situation cannot be so completely defined in terms 
of B alone. It is certain, however, that | U | will 
show essentially exponential behavior in any region 
where the “height of the barrier,” i.e., the amount 
by which the Y curve lies to the left of the line at 
— B, is greater than A. 

This sort of general physical consideration about 
the U curve leads, on being put in more precise 
mathematical form, to the phase integral methods. 
Unfortunately, no phase integral method can claim 
validity for this model except in cases of trapping. 
In general, the Eckersley phase integral method for 
untrapped modes requires that the Y curve be an 
analytic function, and the bilinear curve obviously 
is not. Most of the values presented are, accordingly, 
the results of exact calculation. 

Figure 3 shows that for negative s the attenuation 
falls rather suddenly to very small values at a certain 
value of g and then quickly approaches zero. This 
indicates the occurrence of trapping. On the other 



Figure 3. Attenuation constant versus anomaly height for bilinear M curve, first mode. 




































230 


CHARACTERISTIC VALUES FOR THE BILINEAR M CURVE 



hand, for positive s, the attenuation constant 
approaches a finite asymptotic value. It is interesting 
to note that this is always definitely less than the 
value s 2 x standard, which corresponds to a single 
straight line of slope s 2 x standard slope. 

It is also useful to know the real part B of the 
characteristic value. Figure 4 shows the complex D 
plane. For g = 0 the Y curve is just standard, and 
as g increases the value of D for each value of s 
traces out a curve; for small values of g all these 
curves practically coincide. For negative s the real 
part decreases steadily as soon as the imaginary 
part becomes very small. For positive s, on the other 
hand, the real part as well as the imaginary approaches 
a finite limiting value, so that each curve has an 
end point. 

Some of the consequences of this behavior of the 
real part can be seen by studying Figure 5. The first 
row of diagrams shows the situation for fixed nega¬ 
tive s and increasing value of g. The first diagram 
shows the standard curve. The next shows a curve 
with a small superstandard section, but — B still lies 
in nearly the same location relative to the dotted 
line which marks where the origin lay for the stand¬ 


ard curve; thus B has increased. The first figure of 
the second line shows how the same thing happens 
for a small substandard section. Thus for small g 
the first order effect is just to add the amount g to 
D, for all values of s. 

In the third diagram of the first row we have a 
case in which the superstandard has a pronounced 




























































CHARACTERISTIC VALUES FOR THE BILINEAR M CURVE 


231 


effect, but trapping has not yet set in. In such inter¬ 
mediate cases B may become positive, but the 
diagram shows a case in which it happens to be 
zero. In the fourth diagram trapping is definitely 
established; B has become negative, and the line 
— B has taken on a definite position relative to Y (0) 
(dotted line). This same relation is maintained for 
larger values of g, as in the last diagram of the top 
row. In the last diagram the “barrier” has become 
much more formidable. This means that the value 
of U just above the barrier is extremely small, and 
thus the attenuation is very small because of the 
small leakage. 

In the second row, as has been remarked, the first 
diagram shows a small substandard section which 
has only a small perturbing effect; — B lies essentially 
at the standard distance from the intercept of the 
extrapolated standard curve. The second shows an 
intermediate case. In the third diagram the limiting 
value of D has been reached, and the line at —B 
has taken its final position relative to the joint of 
the Y curve. In the last, larger, diagram g has 
become much larger, but —B has still the same 
position relative to the joint. 

The difference between the last two diagrams is 
essentially the increase in the strength of the surface 
barrier. The structure of the height-gain curves near 
and above the joint is practically the same in the 
two cases. The very thick barrier in the last case 
causes the intensity near the earth’s surface to be 
extremely small. This particular kind of height-gain 
effect can be more suggestively referred to as depth 
loss. The amount of this depth loss is very large: 
the first 200 ft of the substandard layer produces a 
loss in the product U (zf) U(zf) of at least 200 db (at 
10 cm), which is about four times the gain for a 
similar height in the standard case. Moreover, this 
loss proceeds at a rapidly accelerating rate, whereas 
standard height gain goes at a decreasing rate. The 
same situation of depth loss in thick nonstandard 
layers occurs in transitional cases, with s positive 
but less than unity. 

In general the results for the first mode for positive 
s can be summarized as follows: 

In nonstandard layers of fairly small thickness, 
less than 100 ft for 10-cm waves, the propagation is 
not markedly different from standard for the sub¬ 
standard case and can have attenuation strikingly 
less than standard for suitable thickness of a transi¬ 
tional layer. 

For thick layers there is a strong depth-loss effect 


in the first mode in both sorts of cases, and the first 
mode cannot be expected to be the dominant term 
in \I> except at great distances. Some other mode, 
which does not suffer from the depth-loss effect, 
although it may have greater attenuation, will be 
the important mode at smaller distances. 

The conclusions for positive s cannot be expected 
to apply unless the lower part of the M curve is 
really sensibly straight Over a considerable part of 
its length. For negative s (trapping) this requirement 
is not so important. 

It was mentioned that other models had been 
employed by various investigators in calculating 
field strength in the presence of a duct. The British 
used an index distribution given essentially by Y = 
(z — z m /m), where m lies between zero and unity. 
When m = y 2 the problem could be treated by a 
phase integral method, which Booker had done. The 
differential analyzers at Manchester and Cambridge 
had been used to obtain the characteristic values for 
other values of m. The linear variation of index had 
been studied by Hartree and Pearcey. In this case 
of linear exponential variation Y = z + Ae~m, where 
A and B are adjustable parameters. This model offers 
the advantage that the index is an analytic function 
of z and also that the modification term approaches 
zero with increasing height. 

An alternative method (Langer’s) for joining the 
two parts of an otherwise bilinear M profile was 
brought up. This method gives a solution in terms 
of Bessel functions and solves the difficulty perfectly 
for joining two straight lines. 

It was inquired whether, in case of positive s it 
had been ascertained that for large g there were no 
roots of the secular equation corresponding to a 
linear M curve having the slope of the lower segment. 
There was the possibility that the root found might 
be one of a possible pair and that there might be 
another solution of the wave equation for positive s 
which had not yet been discovered. 

The author replied that the roots varied continu¬ 
ously as g varied and that the investigation had 
dealt with the root obtained when starting with the 
first standard value for g = 0. What happened with 
increasing g when the start was made from some 
other standard value of g = 0 was not known defi¬ 
nitely, but the effects were believed to be peculiar. 
It is expected that there may be some values lying 
fairly near the s squared value for the imaginary 
part. They are not considered to lie close to the s 
squared value for the real part, as they would for 



232 


CHARACTERISTIC VALUES FOR THE BILINEAR M CURVE 


the simple assumption previously mentioned—that 
when the joint is very high the upper segment can 
be forgotten and the curve can be assumed to be a 
single line all the way. This is believed incorrect, 
because when the result is derived by taking only 
the first terms in the asymptotic expansions, com¬ 
puting a small correction from the next terms in the 
asymptotic expansions produces terms which are 
infinite compared to the first terms. This means that 
the value s squared times D is an impossible one. 
It may well be that there are results with s squared 
times A plus some different value of B rather than 
simply s squared times B, but these have not been 
investigated. This does not occur for the first mode, 
which is all that this report covers, but it may 
happen that some other mode goes over to that 
value. Any mode which does so would probably not 
suffer from depth-loss effect and would be the 
important mode close in when there was a thick 
layer with positive slope. 

The need was pointed out for stressing the differ¬ 
ence between “completely trapped” modes and 
“leaky” modes. With completely trapped modes the 
field decreases exponentially with height, and the 
power carried by each mode is finite, but with leaky 
modes the field increases exponentially with height, 
and the power carried by each mode is infinite. This 
means that completely trapped modes may exist 
separately, but leaky modes may not. The expan¬ 
sions of fields in terms of leaky modes are thus 
essentially mathematical and from physical considera¬ 
tions it is no longer possible to anticipate that these 
expansions would be convergent; the question of 
convergence has to be settled formally. The reac¬ 
tions of trapped and leaky modes to small perturba¬ 
tions are quite different. The former are relatively 
insensitive and the latter are very sensitive. In 
considering the field at a certain distance from the 
transmitter, it must be ascertained whether the 
relevant modes are affected by changes in the 
dielectric constant at heights large compared with 
this distance; if this is the case particular care must 


be taken in proving the sum to be still the same, 
since even a perfectly reflecting layer at such great 
heights can have little effect on the field in the 
region of interest. 

It was noted that these remarks pertained to a 
phenomenon which had greatly puzzled the investi¬ 
gators for several months. The trouble occasioned 
by the concept that infinite energy is carried by a 
mode does exist. This means that the formula in 
terms of modes is valid only if all those modes are 
summed that make any appreciable contribution. It 
becomes extremely difficult to carry out the summa¬ 
tion when there are numerous modes, as they begin 
to cancel each other more and more with progress 
into that region. This occurs in leaving the diffraction 
region to which this work is meant to apply and in 
approaching the optical region. The question of what 
a small departure from the shape of the curve at 
great heights does is something which was very 
troublesome during studies made some months ago. 
There is no doubt that a small departure from a 
smooth shape of the M curve has an enormous 
effect on the results if it occurs at a great height. If 
the departure is located high enough it need not 
amount to more than a millionth of an M unit to 
spoil the calculation completely. That is because it 
is a reflecting layer similar to the Heaviside layer, 
and if placed high enough it not only can reflect to 
enormous distances but also becomes extremely 
effective. It was decided not to give this effect too 
much concern as all these calculations are made on 
the basis of horizontal stratification. Doubtless all 
sorts of small departures from a smooth curve occur 
at various rather large heights, but they do not occur 
perfectly stratified over areas of hundreds of square 
miles, and only such perfectly stratified departures 
could cause embarrassing results. Accordingly it was 
decided that such fluctuations as occur probably 
cause fading or fluctuation but do not cause the 
particularly troublesome effect mentioned, because 
they are local disturbances which are not stratified 
over large areas. 



Chapter 20 

INCIPIENT LEAKAGE IN A SURFACE DUCT 


201 CALCULATIONS FOR THE FIRST 
MODE OF THE BILINEAR MODEL 

A recent interchange of ideas on problems of 
mutual interest with members of the wave 
propagation group of the Radiation Laboratory 
prompted the author to investigate the variation of 
the attenuation constant (or space decrement) a(h) 
of the first mode with the duct height h and negative 
index gradient a of a surface duct (see Figure 1). 



Figure 1. Variation of the attenuation constant with 
duct height. 


The attenuation constant is defined as the constant 
a which occurs in the factor as: (1 /'s/d) e~ ad , 
giving the variation of the amplitude with range d. 

The results are shown in Figure 1. In this figure 
the attenuation constant a(h) is expressed in terms 
of the attenuation constant for zero duct height 

a By C. L. Pekeris, Columbia University Wave Propagation 
Group. 


a(0). In Figure 1 the curve for 5 < 1 was computed 
from a formula developed by Freehafer and Furry 
of the Radiation Laboratory: 

a(0) V b) 90 

~(l + — __ • (1) 

V ^ b) 1,2(50 K J 

d = h(k 2 b)* . 

h = duct height; 
a = —dM/dz inside the duct; 
b = dM/dz above the duct; 
k = 27t/X. 

It was felt that this equation could be used up to 
5 equal to about 1.3 but not beyond this value. 

The curves on the right for 5 > 2, for which a 
condition of nearly complete trapping is approached, 
were obtained as follows. The secular equation for 
the proper value of A (a ^ I m A), is 

H?(p) _ flfW/f-f (g) + RJf 0>)g ?(g) = Q 

Hf(s)HJ\>(q) + HJf(s)H^(q) 


where 

Here 


where 


2 k 3 2 k /. i j \ a ^ /o\ 

( l = Ta A '’ V = ra {A + ah), ’ S = yq ’ y= b (3) 

is transformed by the substitution 

/2 b\i 

q = e arl2 x, p (ad + /3)b /3 = ahl ^ \ (4) 

into }{p) — Fix) = 0 , (5) 


with 


f(p) = 


tff(p) 


Fix) = 


Ujyx) Vix) + V(yx) Uix) 

e i*i3 \’(yx) Uix) — U(yx) Vix) 


( 6 ) 


Uix) = Iiix) + »(*) , 

Vix) = I t ix) + e^I-tix) . (7) 


233 










234 


INCIPIENT LEAKAGE IN A SURFACE DUCT 


Assume now that 


V = Po + A , (8) 

where po is a constant, which is to be chosen in such 
a manner that A is small in comparison to p 0 in the 
region under consideration. Expanding equation (5) 
in a power series in A, one obtains as a first approxi¬ 
mation for A: 


F(x 0 ) - f(p 0 ) 

/(Po) 


(9) 


and for a second approximation 



Ax/W F{X0) S i 

2 f(po ) ^ /(po) J ' 


(10) 


These expressions can be computed with the aid of 
the WPA Tables (unpublished) for the I functipns 
with real argument. The curves in Figure 1 were 
computed down to values of 8 such that A 2 did not 
deviate appreciably from Ai. 

Conclusion. From the computed attenuation for a 
surface duct it appears that, for the first mode, 
when 6(= hk*b*) is less than 1, trapping is less than 
2 per cent and that when 8 = 3 to 5 (depending on 
the negative gradient a), trapping is 98 per cent 
complete. (For the meaning of the constants see 
Figure 1.) There is therefore a rather narrow range 
of values of the parameter 8 (1 to 4) within which a 
rapid transition takes place from a condition of 
negligible trapping to a condition of nearly complete 
trapping. This result may have a bearing on the 
observed fading which is associated with ducts. 


202 CALCULATIONS FOR THE SECOND 
AND HIGHER MODES 
OF THE BILINEAR MODEL 


segment of the M curve have been tried but were 
found to involve h functions which are beyond the 
range of existing tables. 

Some results on the characteristic values are shown 
in Figures 2 and 3 (for a definition of natural units 
see preceding articles). In Figure 2 the slope of the 
lower segment of the M curve is the negative of the 
standard slope, while in Figure 3 the ratio of the 
slope of the lower segment to the standard slope is 







\ 














\ 

1 

Y 


s 

1 

Y 











\ 



\ 

B 3 






r 





\ 

y 


\ 





A 



% 

V* 



|\ 


1 

f\ 



/ 

«' 


>bT 

3- 


\ 

3 —< 

3- 



\ 



/I 





N 

\ 







/ 

7 






\ 

\ 



\ 

V 


/ 

»^3 







\ 

\ 


















\ 












k 














V 





1- 

r 






























A 










s 



\ 













3. 











Az 






i 

k* 











\A. 

o 



\ 











\ 



\ 

i 

V 











\ 



\ 


i 

V 3 









V 

2^. 

_ 1 _ 1 



^ 




o ————L—.T°-J—i— 

0 12 3 4 5 6 7 


9 — 


The Analysis Section of Columbia University Wave 
Propagation Group has undertaken the computation 
of the characteristic values and height-gain functions 
for the second and higher modes of a bilinear model 
M curve. The first mode of the bilinear model is being 
treated at the Radiation Laboratory. The computa¬ 
tions were carried out with the aid of tables of h 
functions prepared by the Harvard Computation 
Laboratory, under the direction of Furry. Our work 
to date has been mainly on surface ducts, in which 
the slope of the lower segment of the M curve is 
negative. Cases with positive slopes of the lower 


Figure 2. Characteristic values of D m for a bilinear 
model, s = — 1 . D m = B m -f- i A m . s 1 = ratio of slope 
of lower segment to standard slope = s 3 . g = height of 
joint in natural units. 

— 's/s. The curves Ai and Bi for the first mode were 
computed at the Radiation Laboratory. An imagi¬ 
nary part A h which is proportional to the horizontal 
attenuation (decrement), starts at g = 0 with a 
value appropriate for a standard atmosphere and 
decreases continuously as duct height g increases. 
Beyond g = 3 the first mode is completely trapped. 
The curve A 2 for the second mode decreases initially 





























































































SECOND AND HIGHER MODES OF THE BILINEAR MODEL 


235 


too but beyond g = 2 is seen to level off to a constant 
limiting value. The real part of the characteristic 
value B 2 also approaches a constant limiting value 
for g greater than 3. These curves were obtained by 
solving the secular equation for D and also deter¬ 
mining the slope dD/dg at each point. The charac¬ 
teristic values curves can also be computed by 
starting first with Gamow’s values appropriate for 


Table 1 . Comparison of exact limiting values of D with 
values obtained from the asymptotic formula.* 


s 

Second mode 

Third mode 


-1 

-0.60 + 2.80f 

-1.06 + 3.60i 

Asymptotic 

-V2 

-0.59 + 2.83i 


Exact 

-0.78 + 2.74 i 

-1.22 + 3.40i 

Asymptotic 


-0.70 + 2.70i 

-1.42 + 4.08i 

Exact 

-2 

-1.00 + 2.60f 
-0.80 + 2.44i 

-1.36 + 3.48i 

Asymptotic 

Exact 




Figure 3. Characteristic values D m for a bilinear M 
curve, s = — V"2*. g = height of joint in natural units. 
s 3 = ratio of slope of lower segment of M curve to the 
standard slope. D m = B m + i A m . 


large g and continuing backwards toward smaller 
values of g, being careful to determine the slope of 
the curves at each point. It is seen from Figures 2 
and 3 that, in contrast to the first mode, these 
branches of the curves for the second and third 
modes do not join on smoothly to the other branches 
which start with standard values at g = 0 and 
approach limiting values for large g. 

This duplicity of the solutions, which was doubted 
at first, was substantiated in two ways. The values 
of A 2 and B 2 at g = 3 and g = 5 in Figure 1 were 
computed at both branches with increasing accuracy 
(up to 10 -5 ), and it was found that the matching of 
the solutions at the duct height and the degree of 
vanishing of the height-gain function of the ground 
improved correspondingly in both branches. This 


1 - s 3 J /8DI = 0 . 

proves that both solutions satisfy the boundary 
conditions. As a second step in testing the reality of 
the limiting points, an asymptotic expression was 
derived for the limiting v-alues, and the values com- 




z/g^ 


Figure 4. Height-gain functions of the second mode 
for a bilinear M curve, s = — V ~2 . z = height above 
ground in natural units, g = height of joint in natural 
units. U 2 (z) = normalized wave function. 











































































































































236 


INCIPIENT LEAKAGE IN A SURFACE DUCT 


puted therefrom were found to be in fair agreement 
with the exact values, as is shown in Table 1. 

The physical nature of the duplicity of solutions 
seems to be as follows. The solutions approaching a 
limiting characteristic value for large duct height g 
correspond to the case where the ground sinks to 
great depths; the other solution corresponds, of 
course, to the limiting case when the height of joint 
rises to infinity. 

The relative importance of the two types of solu¬ 
tion will depend on the ranges and heights considered. 
At sufficiently great ranges the solutions with the 
smaller value of A m will predominate, but the greater 
the height considered the farther must one recede 
from the source before the initial advantage of the 
limiting solution due to a greater height gain is 
overcome by the stronger horizontal attenuation. 
The greater height gain of the limiting solutions at 
high elevations is illustrated in Figures 4 and 5. In 
these figures, the height-gain functions for the limit¬ 
ing solutions are drawn in solid lines, those for the 
Gamow solutions in dashed lines; and the unit of 
height is the duct height. It should also be pointed 
out that the normalization condition applied was 

jul(z)dz = g , (13) 

so that, if a comparison of height-gain functions of 
solutions of the same class for different values of g 
is desired, the plotted values should be divided 
by Vg. 



Figure 5. Height-gain functions of the second mode for 
a bilinear M curve, s = — 1 . z = height above ground 
in natural units, g = height of joint in natural units. 
U-l (z) = normalized wave function. 













































































Chapter 21 


THE SOLUTION OF THE PROPAGATION EQUATION 
IN TERMS OF HANKEL FUNCTIONS a 


T he calculation of the field strength in the atmos¬ 
phere depends upon finding a solution of a wave 
equation incorporating the propagation properties of 
the atmosphere and satisfying the boundary condi¬ 
tions at the surface of the earth and for large heights. 
This chapter shows how the wave equation, for cer¬ 
tain specified conditions, may be solved in terms of 
Hankel functions. 

Let 


z = height of receiver above earth’s surface, 
h t = height of transmitter, 
d = great circle distance between source and 
receiver, 

X = wavelength, k — 2 t/\, 
f = frequency, co = 2 tt/, 

M = modified index of refraction, 
a = radius of the earth. 

Under the simplifying assumptions of horizontal 
stratification, slight variation of refractive index in 
a wavelength, smooth earth’s surface, the plane earth 
representation, and the use of the simplified boun¬ 
dary condition = 0 for z = 0, which eliminates 
the polarization of the source, the field of a (dipole) 
source is described by a scalar wave equation: 

A 2 ^ + k 2 M 2 V = 0 , (1) 

plus appropriate boundary conditions. Separation of 
equation (1) in cylindrical coordinates leads to the 
formal expansion for the field of a dipole source: 

oo 

¥ = eiwt - l7rff<§> (kd cos a n ) U„(z)U n (h,) , (2) 

n - l 

where Re (cos a n ) > 0 . 

Here the characteristic values sin 2 a TC and the 
(normalized) characteristic functions U n (z) satisfy 
the equation 

rMl 

+ k 2 [sin 2 a + M 2 \ U = 0 , (3) 


a By Lt. W. F. Eberlein, USNR, Office of the Chief of Naval 
Operations. 


plus the boundary and normalization conditions: 

17(0) = 0 (3a) 

eiutU{z) represents an outgoing wave for large 

positive z . (3b) 

lim f " U 2 dz = 1 . (3c) 

Usually sin 2 a is small, kd is large, and one has 

H'S (kd cos a n ) 


( 2 - ) 

\7r kd cos a n J 


L— i(kd cos arc) 


dkn cos oc n 


e —ikd (i — (i/2) sin an) 


(4) 


The exponential decay factor of the horizontal waves 
thus has the form 


exp —- I m (sin 2 a n ) J , 

and the sin 2 « n values evidently lie in the upper half 
of the complex plane. 

The problem is then to find the characteristic 
values and characteristic functions of the system (3) 
for a given dependence of modified index of refraction 
upon height. For a ground-based duct of height h 
with an M curve being made up of two line segments, 
the upper having standard slope, equation (3) 
becomes 

d 2 TJ 

+ k 2 [A + y(z)] U = 0 , (3') 


where 

y{z) = 2ai(z — h) , 0 < z < h , 
y{z) = 2 a 2 (z - h) , z > h , 

A = sin 2 a + 2 a 2 h , 

ai = i' 

The linear change of variable 

Xl = (I ttl ) 3 ^ + 2ai ^ ~ ^ 


237 













238 


THE SOLUTION OF THE PROPAGATION EQUATION 


inside the duct, and 


x 2 = Q a'j [A + 2 a 2 (z — h)] 


above the duct reduces equation (3') to 
d 2 U 


dx‘ 


+ xU = 0 , 


( 3 ") 


whose general solution is 


U 


_ jAihi(xi 

\A 2 hi(x 2 


) + B\h 2 (xi) 

(x 2 ) + B 2 h 2 (x 2 ) 


The “h/’ functions are expressible in terms of Hankel 
functions of order 

h,{x) = (J)‘z*//f (§*,) 0 = 1,2) . (5) 

Condition (3b) is satisfied by setting A 2 = 0. Ai and 
B\ are determined by the requirement of continuity 
of U and dU/dz at z = h. 




( 6 ) 




The characteristic values A then appear as the roots 
of the equation 

(A — 2a ih) 


U( 0) = AJti 

-T B\h 2 


[te 
[(£) 


■ 


’ (A — 2aji) 


]-■ 


( 7 ) 


A’s so far as possible. Due care must be exercised in 
dealing with the branches of the multiple-valued 
approximations appearing, as well as with the 
so-called “Stokes phenomenon.” For example, in 
deciding between the two rival asymptotic approxi¬ 
mations 

ff < ?> (W) £* (~J e~ l,w -^ l2 > , 

( 9 ) 

Hf ( W ) 3* + e .W+ 1W12)] ( 


both formally valid in the common domain 0 
arg W < 7r, one employs the first when arg W < 
tt/2, and the second when arg W > w/2. The ambi¬ 
guity on a “Stokes line” (arg W = x/2) apparently 
must be resolved by taking the mean of the two 
expressions when their difference is important, as it 
is when strongly trapped modes exist (oi < 0). 

The nature of the results obtained is illustrated 
in the important case of complete inversion (cq < 0). 
For simplicity set 



( 10 ) 


Then 

I ( P + l)» - (l - %) p = ^ , 

\ «2/ V 

J^arg (p + 1)>|J 

II 1 + ie-^ f + 1)1 + -1) <* 

U \ ( u ) 

= 0 , I-< arg p<ir - St 


The constant factor B 2 appearing throughout is 
determined by the normalization condition (3c), 
which takes a peculiarly simple form in this case, 
since (3”) implies the identity 



Owing to the present lack of adequate tables of 
the H ( ( ) or hj functions for complex arguments and 
the complicated nature of equation (7), one is forced 
to employ asymptotic expansions to determine the 


III 1 + i e - 2t ^ + » i + h-Mi-ij) pl 

= 0 , (arg p^w) . 

(n a positive integer) 

The corresponding regions of validity are indicated 
in Figure 1, which also shows the dependence of one 
characteristic value on a for a particular ratio a 2 /a\. 
If one numbers the characteristic values p n in order 
of increasing imaginary part, those for which n is 
greater than some integer are defined by equation 







THE SOLUTION OF THE PROPAGATION EQUATION 


239 


I. There is an infinite number of these “Eckersley” 
or “leaky” modes. Equation II joins on smoothly to 



Figure 1. Diagram showing the locus of p in the com¬ 
plex plane of cr varies. 


I and defines a finite number of “transitional” or 
“semileaky” modes. 

Equation III defines the strongly trapped or 
Gamow modes for which 0 < I m (p) <3C — Rd(p) < 
1. In this case the characteristic values lie almost 


upon a Stokes line (arg p = t — 5). The approxi¬ 
mations valid aboye the line yield II; the ones valid 
below yield 

IV 1 + ie~ iia ' p + = 0 , or 

(p + 1) ! = (n - J0 - < 1 (n = 0,1,2 • • • ). 

<J 

Thus in the Gamow case IV makes I m (p) = 0 while 
II yields almost the same real part, but a very small 
positive imaginary part for p. The mean approxima¬ 
tions effectively yield III whose roots are essentially 
the mean of the roots of II and IV. This averaging 
process checks closely with an exact calculation based 
on the (unpublished) WPA tables of Bessel functions 
of order }/£ for real and pure imaginary arguments. 
It is to be noted also that IV determines the number 
of strongly trapped modes as the largest integer n 
such that (n — M) ir/<r < 1. 

The characteristic value problem may be regarded 
as essentially solved in the cases of leaky modes (I) 
and strongly trapped modes (III). In doubt still is 
the question of the transition between III and II; 
this uncertainty plus the fact that actual determina¬ 
tion of the roots of II is much more complicated 
than in the other cases, and that in case II the 
arguments of certain of the Hankel functions lie so 
close to the origin as to make doubtful the validity 
of the asymptotic procedure—all these considera¬ 
tions indicate that resolution of the transitional mode 
question awaits appearance of adequate tables of 
the Hankel functions for complex arguments. 






























































Chapter 22 

ATTENUATION DIAGRAMS FOR SURFACE DUCTS 


T he horizontal attenuation (decibels per unit 
distance) of a signal under assumed propagation 
conditions not only is of intrinsic interest but is one 
of the simplest quantities to verify experimentally. 
In terms of the wave equation formulation this 
attenuation is proportional to the imaginary part of 
the characteristic value associated with the mode 
dominant in the region of space in question. No one 
mode may necessarily be dominant, and in certain 
regions a weakly attenuated mode may be outweighed 
by a mode more strongly attenuated but with a 
stronger initial excitation. Well inside the shadow 
zone, however, the “first” or least attenuated mode 
is frequently dominant. The results presented apply 
primarily to this situation. 

The type of M curve considered is the bilinear 
model in which the M curve consists of two straight- 
line segments, the upper being assumed to possess 
standard slope. This model M curve is completely 
characterized by two parameters: duct thickness and 
M deficit. Figures 2, 3 and 4 refer to three 
frequencies (200, 3,000, and 10,000 me) and super- 



Figure 1. M- curve model. 

standard conditions corresponding to ranges of 1 to 
100 M units in M deficit and 10 to 1,000 ft in duct 
thickness. 

a By Lt. William F. Eberlein, USNR, Office of the Chief 
of Naval Operations. 


The solid curves are contours of constant decibel 
attenuation (of the first mode) per thousand yards. 
One enters the diagram with given values of duct 
thickness and M deficit and interpolates between these 
contours to obtain the corresponding attenuation. 

The dashed curves are contours of constant “trap¬ 
ping index” (number of classically trapped modes). 
In terms of the standard notation their equation is 

10 6 f . . 9A 2 / 1\ 2 1 

M deficit = -g- (* - 4 J _ ■ 

Their significance lies in that they furnish an indica¬ 
tion of the number of modes other than the first that 
must be taken into account. If, for example, the 
bilinear M curve in question corresponds to a point 
midway between the m = 1 and m — 2 contours, 
the first mode is strongly trapped and the second 
mode attenuation is reduced considerably below 
standard. Which mode is dominant then depends 
critically upon the heights of transmitter and 
receiver, and the simple first mode picture becomes 
incomplete except at great distances and small 
heights. 

If one attempts to apply these results to simple 
surface ducts differing from the idealized bilinear 
model one should first approximate the actual M 
curve by a bilinear curve and then enter the diagram 
with the values of M deficit and duct thickness 
corresponding to the idealized curve. How to make the 
best bilinear approximation to a given M curve is 
an important but still open question. 

Except for the 0.01- and 0.001-db contours, which 
were computed by an asymptotic method, the attenu¬ 
ation contours were cross-faired from preliminary 
Radiation Laboratory calculations. The author 
wishes to thank the Radiation Laboratory group, 
and Doctors Freehafer and Furry in particular, for 
permission to use their data. 


240 







ATTENUATION DIAGRAMS FOR SURFACE DUCTS 


241 


l 



Figure 2. Horizontal attenuation of first mode and trapping index, 10,000 me, standard attenuation ( 0 M deficit): 
1.83 db per 1,000 yd. 

















































DEFICIT 


242 


ATTENUATION DIAGRAMS FOR SURFACE DUCTS 



Figure 3. Horizontal attenuation of first mode and trapping index, 3,000 me, standard attenuation (0 M deficit): 
1.23 db per 1,000 yd. 


































































ATTENUATION DIAGRAMS FOR SURFACE DUCTS 


243 



DUCT THICKNESS IN FEET 


Figure 4. Horizontal attenuation of first mode and trapping index, 200 me, standard attenuation (0 M deficit): 0.498 db 
per 1,000 yd. 
































































Chapter 23 

APPROXIMATE ANALYSIS OF GUIDED PROPAGATION 
IN A NONHOMOGENEOUS ATMOSPHERE 4 


T he military importance of guided or 
“anomalous” propagation in a stratified atmos¬ 
phere is now well known. Unfortunately, or perhaps 
fortunately, the problem cannot be treated with the 
aid of known and tabulated functions except in some 
special cases because the exact field distribution with 
height is a function of a function, namely a function 
of the distribution of the modified index of refraction. 
For each distribution of this index with height we 
should have a curve for the field distribution. These 
curves will look similar in a general way and yet 
they will differ in detail; but in this particular 
problem we are not much concerned with details. 
Even if we had exact solutions we should still want 
some generalized way of expressing pertinent infor¬ 
mation. 

An approximate analysis of field distribution in 
terms of master curves, depending on one, or at 
most, two parameters, will be discussed. For example, 
if we have atmospheric conditions favoring forma¬ 
tion of a guiding layer immediately above the ground 
or sea level, then we can try to represent the field 
distribution with height with the aid of the master 
curve shown in Figure 1. This curve depends on only 
one parameter, H, so chosen that in the layer between 
{}/%) H and H, the field intensity does not deviate by 
more than 6 db from the maximum. 



O 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 

h/H 


Figure 1. Master curve for field distribution with 
height inside a duct. 

This particular curve is chosen for the first trans¬ 
mission mode, and it has been suggested by the exact 

a By S. A. Schelkunoff, Bell Telephone Laboratories. 


analysis of guided waves in a homogeneous layer. 
In this case of sharp discontinuity in the index of 
refraction the field distribution curves are sinusoidal 
in the layer and exponential outside. The position 
of the maximum of the sinusoidal portion of the 
curve and the relative rate of decay of the exponen¬ 
tial part depend on the ratio of the wavelength to 
the thickness of the layer and on the amount of 
discontinuity in the index of refraction. In Figure 2, 
curve 1 is identical with the curve in Figure 1; curve 
2 shows what happens if the wavelength is doubled; 



0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 


h/H 

Figure 2. Master curves for wavelength X (1), 2\ (2), 
and Yl X (3). 

and curve 3 corresponds to the case in which the 
wavelength is halved. If the wavelength is 2)/4= 

3.3 times as large as the wavelength corresponding 
to curve 1 or larger, no guided waves are possible 
with the field intensity vanishing at the ground or 
sea level. 

The situation is different if the index of refraction 
is allowed to vary continuously and to diminish 
indefinitely. Suppose, for instance, that the lapse 
rate of the index of refraction is constant. We don’t 
expect any critical wavelength in this case; as the 
wavelength increases we expect the field to spread 
out more and more. In fact, we expect the shape of 
the field distribution curve to remain the same, 
namely to be determined by that solution of 

(«] E (1) 

which vanishes at h = 0. In this equation 


244 































GUIDED PROPAGATION IN NONHOMOGENEOUS ATMOSPHERE 


245 


E = the electric intensity; 
h = the height; 

€ = the modified dielectric constant; 
o) = the radian frequency; 

= the phase constant in the direction 
parallel to the stratification. 

We can try to approximate this solution by a curve 
of the type shown in Figure 1 in which case the 
problem is to select a proper value for H. The ques¬ 
tion may be raised regarding our preference for this 
particular curve rather than for curve 2 or 3 in 
Figure 2. We shall return to this point later; for the 
present we shall merely point out that curve 1 
occupies a “mean” position among other curves of 
this type. 

There are two methods for selecting H. In one 
method H is defined as that value of h for which the 
coefficient 0 2 — coVe(/i) in equation (1) vanishes. 
This value of h separates the region in which the 
solution of equation (1) is “more” or less sinusoi¬ 
dal” from the region in which the solution is “more 
or less exponential.” This definition leads to one 
equation connecting H and 0. Next, the stratified 
region 0 < h < H is replaced by a homogeneous 
region in which the dielectric constant is equal 
to the average value of e(h) in the interval (0 ,h). 
If we impose the requirement that curve 1 repre¬ 
sents the exact field distribution under the new 
conditions, we obtain the second equation for H and 
/3. Eliminating js and expressing the result in sym¬ 
bols approved by the wave propagation committee, 
we have 

f H q v in 6 

Hi M(h ) dh - H 2 M(H) = X 2 . (2) 

If the lapse rate of M is constant, this equation gives 



Ey = (const) t/i [Ji(U) + J-\ (C7)] Ey = sin p p< f 

C/ = 37 4 {l_3~J § Ey = ^l>e-P p> £ 

Figure 3. (1) Exact solution normalized to have min¬ 
imum value of unity. (2) Approximation. 


solutions of equation (1) minimize and reduce to 
zero the following function: 

I = |8 2 f E*dh -o>V (o) ^ dh 



(5) 


In deriving this equation we should remember that 
we are concerned with solutions which vanish at 
h = 0 and h = oo. Hence, if we wish to approximate 
this solution by a function of one parameter H, we 
eliminate H from the following two equations 

I = 0 , 4ir = 0 • («) 


If, for instance, we wish to approximate the field 
distribution by the master curve in Figure 1, we solve 


// 2 1^- - HP = 
dH 


9 X 10 5 , 
128 


(7) 


If M ( h ) is proportional to h 2 , then 

H = 18X» • ( 4 ) 

If the lapse rate of M is constant, the exact solution 
may be expressed in terms of Bessel functions. 
Figure 3 shows the exact and approximate solutions. 
For this comparison I am indebted to J. E. Freehafer 
of the Radiation Laboratory. 

The second method is based on the fact that the 


where 


p = -jf M si 
" 55 ■=/, 


M exp 


- 37r/l 
- 

4 H 

— StH 


dh 


dh . 


2 H ‘ ( 8 ) 

By this variational method the numerical coefficient 




















246 


GUIDED PROPAGATION IN NONHOMOGENEOUS ATMOSPHERE 


in equation (3) is found to be 64 rather than 65. 

The great advantage of the variational method 
lies in the fact that, if we wish, we can increase the 
number of parameters in the approximating func¬ 
tion. For example, we can assume 


E(h) = sin 


0 < h < H 


* Sr^] ’ h > H ’ (9) 

without specifying that 0 = = 37r/4 as we did 

in obtaining the curve in Figure 1. We should then 
calculate H, 0, and \p from 


= sin 0 exp 


[- 


I = 0 , 


dl 

dd 


= o, 


di 

dxp 


= 0 


( 10 ) 


However, aside from the labor of solving these 
equations and having to deal with more complicated 


results, we shall lose the advantage inherent in a 
description of the field in terms of only one easily 
understood parameter. The most we could hope for 
from an analysis of these equations is a somewhat 
better choice of the master curve for the type of 
atmospheric conditions which are the most likely 
to occur. 

The obvious general conclusion from equations 
(7) and (8) is this: if M(h) is multiplied by a con¬ 
stant factor, the effect on H is the same as that 
obtained if we divide X by the square root of this 
factor. If M is proportional to h n , then H is propor¬ 
tional to \ 2/(w+2) . Since the gain of the guided wave 
over a free space wave is proportional to \p/H 2 , 
where p is the distance from the transmitter, the 
gain is independent of the wavelength when M(h) 
is proportional to h 2 . For a uniform lapse rate the 
gain varies inversely as one-third power of the 
wavelength. 




Chapter 24 

SOME THEORETICAL RESULTS ON NONSTANDARD PROPAGATION 


241 PROPAGATION IN THE OCEANIC 
SURFACE DUCT 

T he analysis section of Columbia University 
Wave Propagation Group undertook a theoretical 
study of propagation in case of surface ducts, which 
have recently been reported to be of common oc¬ 
currence in oceanic areas. The M curve chosen was 
M(h) = 346.4 + 0.036 h + 43e-°- 171 , (1) 

where the height h is expressed in feet. This curve 
has an M deficit of 43 units and a duct height of 48 
ft and is considered to be representative of condi¬ 
tions prevailing around Saipan when the wind is of 
the order of 10 to 20 mph. 

The analysis was based on the phase integral 
method. The standard W.K.B. (Wentzel-Kramers- 
Brillouin) version of the asymptotic solutions of the 
wave equation 107 had to be extended in two ways. 
One was in the adoption of LangeEs form of the 
asymptotic solutions, 449 which enables one to bridge 
the “gaps” around the turning points. The other, 
and more important, development was in the exten¬ 
sion of LangeEs method to handle a case with two 
turning points. This was accomplished by joining 
the solutions from each turning point at the duct 
height. The resulting solution agrees with Gamow’s 
for completely trapped modes but deviates from it 
when leakage begins. For leaky modes the standard 
Langer solution is adequate. 

Coverage diagrams were computed for the S and 
X bands and for transmitter heights of 16 and 46 ft. 
In case of the S band, it was found that the first 
mode was nearly trapped, while the second mode 
was considerably leaky with a decrement of about 
3 db per nautical mile. The two modes were com¬ 
bined, and coverage diagrams were computed over 
ranges and heights such that the second mode 
contributed no more than 25 per cent to the total 
field. 

In the case of the X band, it was found that the 
first two modes were completely trapped, the third 
mode nearly trapped, while the fourth mode was 
leaky with a decrement of over 3 db per nautical 
mile. In computing the coverage diagrams for the X 

a By C. L. Pekeris, Columbia University Wave Propagation 
Group, Analysis Section. 


band, the four modes were combined over such 
ranges and heights that the fourth mode did not 
contribute more than 25 per cent to the total field. 


242 CHARACTERISTIC VALUES FOR A 
CONTINUOUSLY VARYING MODIFIED 
INDEX 

In the theoretical treatment of nonstandard prop¬ 
agation by the method of normal modes, one is 
confronted with the task of solving the differential 
equation for the height-gain function U(Ji) given by 
equation (2), which, it will be noted, is identical with 
equation (8) in Chapter 25. 

Um(h) + k> [y(h) + A w ] U m (h) = 0 , 

2x ( 2 ) 

k = y , y(h) = 2 X 10 ~«M(h) , 


by asymptotic methods, the characteristic value 
A m is determined, to a first approximation, by the 
condition that 

kjVyih) - y(hij dh = v m ^ tt (^m - ^ , (3) 
A m = -y(hi) . (4) 

In order to solve equation (3) one has to find a 
value hi, which is generally complex, such that when 
y(hi) is substituted in the radicand and the integral 

hi _ 

Vy(h) - y{h{) dh = F(hi) (5) 

evaluated, the result should be purely real, and equal 
to v m /k. In case of a surface duct, F(hi) is real and is 
a continuously increasing function of its argument 
for real values of hi ranging from zero up to the 
duct height h 0 . In order for F(hi) to increase beyond 
the value F(h 0 ) and still to remain real it is found 
that hi must be complex; i.e., the path in the complex 
/ii-plane along which F(hi) is real consists of the 
portion of real axis 0 ^hi ^ h 0 followed by a curve 
in the fourth quadrant. 

In case of substandard refraction, F(hi) is real 
only for complex values of hi, and the method of 
solving equation (3) to be explained presently is 


247 





248 


THEORETICAL RESULTS ON NONSTANDARD PROPAGATION 


particularly helpful in this case. 

Let 

y(h) = 2 /( 0 ) + hi h + 6 2 6 2 + — + 6 n 6” + —, 

* dh f AA 1 7 —26 2 

h = Ty i - h = Q)= T l ’ h = ~b^’ 


h = 


( — 66361 4" 1262 2 ) 
61 5 


7 (1206 1 6 2 6 3 - 246i 2 6 4 - 120 6 2 3 ) 

h = - j-j -- , etc. 


= e 


\2kh) ’ 


A m + 2/(0) 


then 

A m = —y(hi) = — 2/(0) + 0 2 + 


(&) 


( 6 ) 


(fes) 8 * 


16 


+ e e 


\ZL 

[375 


[I <*■>’ - 155 <*■»] 




33 

175 


(ht) (fe.) + 




,(7) 


h 1 = —few + -, (8) 


where 


As a further check, we treated the case a = +20, 
X = 0.6356, for which Pearcey and Whitehead 166 
give a value Ai = —10.21 + 1.07 X 10 _1 H\ Equa¬ 
tion (7) yields Ai = —10.22, while the imaginary 
part obtainable from Gamow’s formula is 1.24 X 
10 _13 L 

It must be emphasized that the value obtained 
from equation (7) should be verified by carrying 

out the integration of F(hi) = J 0 ^/y(h) + A m dh. 
While doing so, one may as well compute 


dhi 


- y 2 y (fci) 


f hl dh 
Jo Vy(h) - 2/(60 ’ 


( 10 ) 


and then obtain a correction to hi by Newton’s 
method. 

The method of solving equation (3) explained 
above has been found especially useful in the treat¬ 
ment of substandard refraction, and to a lesser extent 
in the treatment of the trapped modes in case of a 
surface duct. In the latter case one can, of course, 
solve for A m directly by computing F(hi) by numerical 
integration. The method is not applicable for the 
leaky modes in case of a surface duct. 

So far the discussion has centered on the solution 
of equation (3), which in itself is only an approximate 
asymptotic formula valid for large values of k. Let 
the value of A m which satisfies equation (3) be 
denoted by Ato ( 0) ; then an improved value for A m 
can be obtained from 



Equations (7) and (8) are of the nature of asymp¬ 
totic formulas; they should be terminated when the 
individual terms begin to increase, and the error in 
A m or hi is then of the order of magnitude of the 
last term retained. 

The following examples in Table 1 illustrate the 
degree of accuracy obtainable from equation (7). 


A = A (t>) 


3e irl *(v m )i /3\ 4/3 
+ 0'A+ 3 \2/ 




( 11 ) 


where 



dh 

V y(h) + A„, (0) 


V ~ dh ’ etC ' ’ ( - 12 - ) 


and the derivatives of y are to be evaluated at h — hi. 


r h i _ 

Table 1. Approximate determination of Ai from equation (7) and the verification that l\/ y{h) + Ai dh = 2.383.* 


a 

X 

Ai from equation (7) 

hi from 

2/(6i) = - Ai 

rhi 

J 0 'V / 2/(6) + Ai dh 

Vi 

-20 

0.6356 

12.360 + 9.775i 

0.3997 - 0.9518i 

2.370 + 0.004i 

2.383 

-10 

0.6356 

4.878 + 6.302i 

0.4745 - 1.1982i 

2.397 + O.OlOi 

2.383 

-5 

0.6356 

1.499 + 4.257i 

0.5691 - 1.4692i 

2.393 + 0.009i 

2.383 

-2 

0.6356 

-0.246 + 2.902i 

-0.764 - 1.787i 

2.363 - 0.008; 

2.383 


y{h) = h + ce~ Xh . 



















Chapter 25 

PERTURBATION THEORY FOR AN EXPONENTIAL M CURVE 
IN NONSTANDARD PROPAGATION 4 


25-1 ABSTRACT 

I n this chapter a perturbation method is developed 
for treating nonstandard propagation in the case 
when the deviation of the M curve from the standard 
(= the M anomaly) can be represented by a term 
ae -Xe , where z denotes height in natural units. The 
method is also applicable to other forms of the M 
anomaly which can be derived from an exponential 
term by differentiation with respect to X; in fact, in 
its region of convergence, it is formally applicable 
to the most general type of M curve, including 
elevated ducts. The region of practical convergence 
of the method ranges from standard down to cases 
where the decrement is a small fraction of the 
standard value. 

The procedure followed is to express the height- 
gain function U k (z) of the k -th mode in the non¬ 
standard case as a linear combination of the height- 
gain functions U m °(z) of all the modes in the standard 
case. 


U t (z) = £] A km U m \z ) . 


( 1 ) 


The execution of this plan hinges on the possibility 
of evaluating the quantities 


/WX) 


[ v - 


(z) UJ(z) e~»dz . 


(2) 


It is shown that /3 nm (\) satisfies the differential 
equation 


d/3 


d>r = 2x + 


[-^ + |(C m » + Z)„ 0) + j + 5 ^ ( Z)M 0 -C„ 0)2 ] , (3) 


whose solution is 


Pnm (X) 


(D 0 + £> 0) + ^_J : (d 0 — D 0)2 
{ n ^ m ' ^ 12 4X v m n ’ 


2VX 


l 


dx -i(D 0 + D,0)-^ + J-(D 0-D 0)2 


y/ a 


g 2 m n ' 12 4* 71 m 


(4) 


Here D m ° denotes the characteristic value of the 
ra-th mode in the standard case. For large X the 
following asymptotic formula holds 

finm ~ 

2 

[X3 + 2X (£>„« + D n «) - 2 + £ (ZV> - Z)„ 0 ) 2 J 


+- 


8 f"3X 3 + 2X (£» m ° + D n °) - i (D m ° - £>„“) 


X 3 + 2X (D m ° + D n <>) - 2 +1 ( D m ° - D 




.(5) 


Having determined the |8 nOT (X) from equation (4), 
or by a numerical solution of equation (3), the 
characteristic values D k and the coefficients A km are 
to be solved from the infinite system of equations 


2] A tm I"(Z>» - DJ) S nm + a & nm (X)l = 0 , 
m= 1 L J 

n = 1,2,3 * • • (6) b 

For this purpose a simple iterative procedure has 
been developed, which has been found to be rapidly 
convergent. The A km are normalized by the condition 


l 


US (z) dz 


1 = 


(7)< 


One can also expand D k as a power series in a 
D k = Dl + aDi + aWl + ■ ■ ■ , 

TV” =-/?«;= e »' 3 2 j (rf-rS ) ’ m±k - 


An alternative expression for D { f is given in equa¬ 
tion (65). 


a By C. L. Pekeris, Columbia University Wave Propagation 
Group. 

b 8 nm = 1, n = m 
8 n m = 0, n dt m. 

c The integral f Q Uk 2 (z)dz diverges when taken along the 

real axis; it converges, however, and to the same limit, when 
the path is a radial line in the fourth quadrant of the z plane. 
In the sequel, whenever an integral is divergent it will be 
understood that the path is suitably modified. 


249 







250 


EXPONENTIAL M CURVE IN NONSTANDARD PROPAGATION 


25.2 INTRODUCTION 

In the theoretical treatment of nonstandard 
propagation by the method of normal modes, one is 
confronted with the task of solving the equation 

+ V -1 ~y{h) + A„] U m = 0 , (8) 

subject to the condition that U m ( 0) = 0 and that 
at h —► 00 , U m should represent an upgoing wave 
only. Here h denotes height in feet. 

y(h) = N 2 (h) - 1 = 2 X 10~ 6 M(h) , k = y , (9) 

and A m is the characteristic value which is generally 
complex. It is convenient to introduce natural units 
of height 

h dN 2 

z = jj,H = ( k 2 q)~\ q = ^ = 2.36 X 10~ 9 cm" 1 , 

D m = A m (-J , (10) 

whereby equation (8) is transformed into 

+ [* + /(*) + A.] u m {z) = o. (ii) 

The term/(z) in equation (11) represents the refrac¬ 
tion anomaly and is equal to zero for a standard 
atmosphere. In the first instance we shall be treating 
the case where 

/(*) = ^- Xz , (12) d 

and we shall later generalize the treatment to deal 
with any M curve represented as a series of Laguerre 
functions. If the original M curve is represented by 
the expression 

M(h) = bh + ae~ ch , b = 0.036 ft" 1 , (13) 

then a and X are obtained as follows: 

a = 2 X 10- 6 (^)* a , X = cH . (14) 

It is to be noted that in contrast to the constants a 
and c in equation (13), which are independent of 
frequency, the constants a and X in equation (12) 
are frequency dependent. For a given observed M 
curve the constants a and X will therefore differ with 


the frequency band used, as will also the height 
represented by one unit of z. 

253 FORMAL SOLUTION OF THE PROBLEM 
BY THE PERTURBATION METHOD 

In order to solve the equation 

+ [z + + o*] u„(z) = 0 , (15) 

we seek a solution in the form 

oo 

U„ = ^A km TJ m \z) , (16) 


where U m °(z) are the height-gain functions of the 
m-th mode in the standard case, which satisfy the 
equation 


d'UJfz) 
dz 2 ^ 

[z + U m °(z) = 0 . 

(17) 

a 

t-H 

II 

—i 

'77 

o 

(18) 

The solutions of equations (17) and (18) are well 
known: 

UJ{z) = C n ui Hi'» (u) , u = | (z + ZV) 

1 ,(19) 


1 Vm d i. (Vm) d- j (^m) 

} (20) 

D 0 — T 

J-Sm — T m 

« i21 ' 3 , r. = (^fj , 

(21) 

where 

J3 iVm) “f“ — 3 iVm) — 0 • 

(22) 

For small z the power series development of U m °(z) 


is useful: 


U m \z) = i ^ A k z k , (23) 

* = 1 



d No confusion should arise from the use of X in equation 
(12) and the standard usage of X to denote wavelength. 


(25) 









251 


EVALUATION OF ^m(X) AS AN INDEFINITE INTEGRAL 


while for large z one may use asymptotic expansion 
of equation (19) 

gi(— u + 5ir/12) . 


*'"(“> - 'Jfu 


1 +*-- 
^ 72 u 


385 

10,368u 2 + ’ 



(26) 


we shall study the function 

F(z) = U n \z) UJ(z) , (31) 

where 

ilm\z) + [z + DJ] U m \z) = 0 , (32) 

Un°(z) + [Z + DA U n \z) = 0 . (33) 

By multiplying equation (32) by U n °(z), equation 
(33) by U m °(z) and subtracting, we obtain 


If now the expansion (16) be substituted into 
equation (15)., we obtain, on making use of equation 
(17), the condition 

2] A ta [(£>* - D m 0) + ae - x *l U m °(z) = 0 . (27) 

771= 1 L J 


£ (Urn 0 u n ° - U m ° {/„») = - (A»° - D n °) U m « t/„°, 

(34) 

UJ U„° - UJ U„° 

= - (£>„» - D„») U m \x) UAx) dx . (35) 


On multiplying this equation by U n °(z), where n is Now it can be verified by direct substitution that 
any integer, and integrating from 0 to °° we get a 

system of equations for the determination of D k and F -\- 2F ( D n + D m + 2 z) + 2 F 
the A km : 




= (Z>„° - D n °) (U m ° U n ° - U m ° U n °) 

r z 

£] ^ *.[(£>* - D m ») S nm + a/UOo] = 0 


= - (£>„» - D„°) 2 f Fix) dx . (36) e 

n = 1,2,3 • • • 

(28) 

From equation (36) it follows that 

A-(X) = J o U m \z) U„°(z) <r x * dz . 

(29) 

F = £ [(2, + D m ° + D n °) F + \ f] 


The characteristic values D k are then obtained as 
the roots of the infinite determinant. 

D k — D\° + aPn , a(3i2 , aPiz , * * * 

aP2i , D k — Z>2° + (XP 22 , ap23 , * * * 

= 0 . 

ocPzi , aPz 2 , D k — Dz 0 + aPz3 , * * * 

• * • , •••,••', • • • (30) 

Having determined D k from equation (30), the 
A km are obtained by solving the system of linear 
equations (28). 


254 EVALUATION OF /W\) 

AS AN INDEFINITE INTEGRAL 

The primary task in the perturbation method is 
the evaluation of the exchange integrals /3 raTO (X) 
defined in equation (29). We shall accomplish this 
by proving that j3 nm (X), as a function of X, satisfies 
a differential equation of the first order for which 
an explicit solution can be given. For this purpose 


+ i (D m « - D n yj° F{x) dx . (37) 

We may also note that 


F(0) = 2{7„°(0) U n \ 0) = -2 , (38) 

_ °o 00 00 

\e~ u Fdz = <r x * (F + \F) + X 2 I e“ Xz Fdz 

=»\r 


Fdz 


(39) 


r 00 r z r z 

/ er* dz / Fix) dx = - l - e~ u / F(x) dx 

i z* 00 c 00 

+ \ / e- X2 F{z) dz = 1 \ e- X2 F{z) dz . (40) 

o xy 0 

e~*° F(z) dz = ~ e~ x ‘ F(z) dz . (41) 


e This is the first occasion in the author’s experience where 
use is made of the fact that the product of two functions, 
each of which is a solution of a distinct second order ordinary 
linear differential equation, satisfies a fourth order linear 
differential equation. 450 










252 


EXPONENTIAL M CURVE IN NONSTANDARD PROPAGATION 


We now substitute equation (37) in the integrand 
of equation (29) and obtain 

Pnm (X) = j o F(Z ) «-* dz = ^ «-»* dz X 
[(22 + D m ° + Dn) F + \ p] 

+ %(D m °-D n yf° F(x)dx\ 


2X 




e~ u F{z) dz 


+ (2a + D b ° + DJ) F + - 


if].- 


-/>[ 

= 1 +J o e- X2 F(z) 


(22 + D n « + DJ) F + | dz 


2\z + X(ZV + D„») +\ X 3 + L (D„« - £>„°) 2 ] dz 


= 1 - 2X 


dfinm (X) 

d\ 


+ /3„ m (X) [x(Z>„° + Z>„») + y + ^ (2V - Z>„°) 2 ] . 

(42) 

It follows that the exchange integral 18 nm (X) satisfies 
the first order differential equation 


d(3nm (X) _ 1 . n /-v \ 

d\ 2X + ^ nm W * 

- ^ + 5 (0„« + D K ») + J (D„» - Z)„») 2 I. (43) 

The solution of equation (43) is 

finm (X) = 


']■ 


Wl 


ez 


CD 0 + D°) + — — — (D® - i>2) 2 

^ ‘ i 2 4 \ rn n’ 


f x dx _£ (Z) o +c o ?3 1 o_ Z) o )2 .... 

/ —— 6 2' w t » ) 12 t 4i l m n> , (44) 

Jo ya: 


25.5 PROPERTIES OF 0„ m (X) 

For small X the solution of the differential equation 
(43) can be started with a power series in X. 


1. n dz m 


A»(X) = - 7~^y S C*'**'* x * , (45) 

\ T m T-n) 


Co = 1 •, c 

c 2 = 
c 3 = 


•(46) 


1 (r w — r n ) 2 ’ 

10Ci — 2 (r m + T n ) 

(r TO — r n ) 2 

14C 2 - 2Ci (r m + r n ) 

(r m — Tn ) 2 

r _ (4n + 2) C w -! - 2 (r w 4- r n ) C w _ 2 - C ra _ 4 
(r. - rj 2 

2. n = m 

finm = 1 + #1 X + B, X 2 + ‘ ‘ ‘ , (47) 

9 4 

r, - : n ° R 0 = _n 2 ( 0 ) 

g 2 ^ ^ ■ Lym > 


1 ft 

B > - n + tb D -“ • 

s --(S J n)[ 2D - ,s - , + s i -']- 


(48) 


For intermediate values of X one may either use 
the integral in equation (44) or integrate numerically 
the differential equation (43). The latter procedure 
was advocated by Hartree. 

For large values of X an asymptotic expansion can 
be obtained directly from equation (43) by writing 
it in the form 

finm (X) = 

dfinm (X) 


- 2 + 4X 


d\ 


X 3 + 2X (Di + D° n ) - 2 + ± (Di - D° n y 


X 3 + 2X (Di + Z)J) - 2 + - (Di - D° n y 


8 3X 3 + 2X (Di + DI) - ± (Di - D° n ) 


+ 


»*] 


X 3 + 2X (Z>» + D° n ) - 2 + i (DS, - my 


>X) 2 ]‘ 


(49) 

















SOLVING VALUES D k AND THE COEFFICIENTS A km 


253 


An alternative asymptotic expansion can be derived 
from equation (44) by partial integration 

fimn * o 


x 3 + 2 \ (d; 


+ B°n)+l 


c ds, - my 


5X 3 + 2X (DS, + D° n ) ~l(D° 


D° n )' 


+ 


X 3 + 2X (DS, + m)+± (DS, 


my 


In doing so one needs to prove that 


I. 


dx - \ K +«S> - z u +4i < - 

Vi 

= '*'.» = o . 


.(50) 


(51) 


tion of equations (30) and (28) is, however, a labo¬ 
rious process which rapidly increases in complexity 
as p exceeds about 4. The following iterative pro¬ 
cedure has been found effective and of the same 
intrinsic simplicity for any value of p. 

To begin with, the p equations in equation (28), 
being homogeneous, do not determine the absolute 
values of all the A km but merely the ratios of (p — 1) 
of them to a p -th one. The absolute values are then 
determined from the normalization condition 


l 


U k \z) dz = 1 = 


00 

2 > 


Let therefore 


C km — 


(7) 


(55) 


We shall state here without proof that 




mm 



x r>0 

m “ 12 


7rN/7T /2\ 3 

~T~\V 


hi (DJ) h 2 (ZV) , 


and the p equations in equation (24) are just suffi¬ 
cient to determine the (p — 1) constants C km and 
D k . We divide the equations in (28) by A kk and pick 
the k -th equation (n = k) to solve for D k , while the 
other equations are used to solve for the C km , as is 
^ 52 ) illustrated in the scheme below for the particular 
case of k = 1. 


where hi and h 2 are Furry’s functions of the first and 
second kind defined as 


>- 

II 

^coTto 

Va: HV (| 

(53) 

>* 

to 

II 

VxHV 

(54) 


Since by definition of D m °, /^(A/) = 0, it follows 
that mm = 0. The proof of equation (51) for n db m 
is left as an exercise to the interested reader. 


256 ITERATION METHOD OF SOLVING 
FOR THE CHARACTERISTIC VALUES D k 
AND THE COEFFICIENTS A km 

In solving equations (28) and (30), which are of 
infinite order, one proceeds by first assuming that 
A km = 0 for m > p, where p is a convenient integer, 
and then evaluating D k and A km , m = 1, 2 • • p. 
Next, one assumes that A km = 0 for m > p + 1, 
resolves for D k and the A km , and the accuracy of the 
results is judged by the agreement between the 
values in successive approximations. The direct solu- 


- —-/ 3 n — C12P12 — C13 /3i3 

a a 


(56) 


(— - — + fe) Cn 

\ a a ) 

— — / 3 l 2 - C13 /?23 — C14 /?24 — 

(— - — + fin) C n 

\ a a ) 

= $13 C12 $23 — C14 $34 — 

(— - — + $44) C14 

\ a a ) 

— ~ $14 — C12 $24 C13 $34 — 

As a first approximation one puts 


^ - Dl ° B 
a ~ IT 


(57) 


(58) 


(59) 


(60) 


Cu = - 


(— ~ — + ft>) , 

\ a a ) 


(61) 






254 


EXPONENTIAL M CURVE IN NONSTANDARD PROPAGATION 


C 13 — 


013 




_ PI 

a 


, etc. , (62) 


to more general types of M anomalies. To begin with, 
if 

f(z) = ae~ Xz + ye~ MZ , (66) 


where the value of Di/a obtained from equation (60) 
is used in equations (61) and (62). Next, one substi¬ 
tutes these values of the C *s in the right-hand sides 
of equations (56) to (59) and resolves for Di/a and 
the C’ s. This procedure has been found to be rapidly 
convergent and is, furthermore, self-correcting in 
case of arithmetical errors. 


then we merely write in equation (28) in place of 
o!0n to(X), [o!0wm(^) H - T0 »w(m)]* Once the finmQ^ 
computed as functions of X, there is no additional 
labor required to deal with an/(z) which consists of 
a sum of any number of exponential terms. If instead 
of/(z) = ae~ Xz we had/(z) = <*ze -Xz , then the corre¬ 
sponding 0' ram (X) would be 


2 57 EXPANSION OF D t INTO A 
POWER SERIES IN a 

When a is small, it is convenient to expand D k 
into the series 

D k = ZV°> + a D k (1) + a 2 D k + • • • . (63) 


It is known from standard perturbation theory that 


D k a) — 


( Tf/i T ic) 

m d= k . (64) 

It is possible also to derive an alternative expression 
for D£ 2) : 

zv» (X) = \ X »*<» (X) 2 + + w • 

z x 


/. 


- -Djfc 0 X - ( x 3 /12) . 


[(i + (X + x) + Z)*«> (X) £>*<» (x) d* 

= X D t »> (X) 2 + l =e c * <0> >' + (>' 3 /i2). 

^\/ X 
x 

f [*.» (x) + (2 + £>,<» (X + x) Jv^ dx. (65) 


r°° 

P'nm (X) = J o (/„»(*) MT** = - ^^.(67) 

If 0 rew (X) is known, d(3 nm (\)/d\ can be computed 
directly from equation (43). When equation (43) is 
integrated numerically, the derivative d(3 nm (\)/d\ is 
computed at each point in any case. Evidently, for 
f(z ) = az k e~* z , where is a positive integer. 

P'nm (X) = ^ U m °(z) U n \z) Z k «-** dz 

= (~) ^ t y ) . (68) 

By successive differentiation of equation (43), it 
is possible to express any high order derivative of 
0 nTO (X) in terms of 0 nm (X). From a purely formal point 
of view we can say therefore that by our method we 
can treat any M anomaly by expanding it into a 
series of Laguerre functions, since these functions 
involve only terms of the form z k e~ Xz . It may be 
pointed out that a single term z k e~ Xz vanishes both 
at the ground and at great height and reaches a 
maximum at z = k/\. Such a single term is therefore 
suitable to represent an elevated duct. 


COMPUTATIONAL PROGRAM 
FOR THE EXPONENTIAL MODEL 


Since the former expression is simpler for compu¬ 
tational purposes, we shall not give here the deriva¬ 
tion of equation (65). 

258 APPLICABILITY OF PERTURBATION 
METHOD TO A MORE GENERAL CLASS 
OF M ANOMALIES 

It is possible to apply the results obtained for the 
case when the M anomaly is of the form/(z) = ae~ Xz 


The Analysis Section of the Columbia University 
Wave Propagation Group has undertaken the com¬ 
putation of 0 nm (X) for X = 0(0.1)4.0 and n, m = 
1, 2, 3, 4, 5. With these functions tabulated, it is 
planned to compute the characteristic values D k for 
such values of a and X that the difference between the 
values of D k obtained from the fourth order deter¬ 
minant and from the fifth order determinant will be 
only about 0.01. The program also calls for the 
computation of the height-gain functions from equa- 









COMPUTATIONAL PROGRAM FOR THE EXPONENTIAL MODEL 


255 


tion (2), since the coefficients A km will be obtained 
simultaneously with the D k when the iteration pro¬ 
cedure is used. This will be possible only in a limited 
region of low altitudes, since at great heights the 
U m °(z ) increase rapidly in magnitude as m is 
increased. However, near the ground the U m °(z) are 
all of the same order of magnitude (= iz) and 



y = N 2 - 1 = 2M • 10" 6 . 

z = ( k 2 q )* h = h/H height in natural units 
(k = 2 tt/\) . 

H = {k 2 q)~% = 7.24 \ CI J (feet) natural unit of height. 


dU k (0) 


dz 



m = 1 



If this derivative of U k {z) at the ground can be 
obtained with sufficient accuracy, then one may use h a 
it to integrate numerically the original equation (11). 

It is well known that, for a given order of the deter¬ 
minant used, the characteristic values D k are ^ 
obtained with higher accuracy than the height-gain A m 
functions. ^ 

It may be added here that /?n(A) computed from m 
equation (44) agrees up to X = 5.0 with the values 
given by Pearcey and Tomlin. 106 X 

The perturbation method will of course become 
inefficient when trapping conditions are approached. 

For such values of a and X, asymptotic methods may 
provide approximate values for the D k , provided 
care is taken at each stage to estimate the order of 
magnitude of the error involved. It is planned to 
map out by a combination of these methods the 
real and imaginary parts of D k in the operationally 
relevant region of the a, X plane. 


1/2 (kq 2 )% d = d/L distance in natural units . 

2 ( kq 2 )~* = 6.69 A cm * (thousands of yards) = 
natural unit of distance . 


anomaly height (height of joint in bilinear 
model) . 

hJH anomaly height in natural units . 

characteristic value (for y = 0 at h = h a ) . 

(&/<?)* A m = B m + iA m characteristic value in 
natural units . 


s~ 2 D (abbreviation for use in computing) . 

eiut — fridl X — iir/4 27j4 


plane wave 


depends 
on X 


X-l £] e~ A <n x + . Um M Um (zs) 


natural units only 


Symbols for Use in 
Theory of Nonstandard Propagation 

q = standard slope of N 2 curve = 2.38 • 10 -7 mr l . 

p = slope of lower section of N 2 curve in bilinear 
model . 


I 


U 2 dz = 1 . 


R = slant range . 
d = horizontal range . 






Chapter 26 

FIRST ORDER ESTIMATION OF RADAR RANGES 
OYER THE OPEN OCEAN 4 


T he most striking nonstandard propagation 
conditions are for the most part associated with 
meteorological conditions which can exist only over 
those portions of the sea which are contiguous to 
extensive land masses. At large distances from the 
coasts, however, low ducts exist which, though they 
never produce strongly locked modes at the usual^ 
radar frequencies, nevertheless modify radar ranges. 
The problem of the low duct has the great advantage 
that conditions are sufficiently near standard that 
numerical solutions can be found in convenient form 
by an extension of the perturbation methods of wave 
mechanics. 

At appreciable distances from land the temperature 
of the air is essentially that of the sea, and the air 
is in neutral equilibrium. Montgomery has pointed 
out that under these conditions there is much 
evidence to support a logarithmic distribution of 
specific humidity. 

The logarithmic distribution of water vapor leads 
to an M curve given by 



where d is the duct thickness, z is the height coordi¬ 
nate, and a is the radius of the earth. If we plot the 
function in the brackets, we obtain the dashed 
curve of Figure 1. 

This type of M distribution is inconvenient because 
(a) the logarithmic term which represents the modi¬ 
fication does not approach zero as the height increases 
as a modification term should; and (b) In (z/d) 
becomes infinite when z = 0. Accordingly it is pro¬ 
posed to replace the function in the brackets by the 
first two terms of its series expansion about the 
minimum. This amounts to substituting for the 
logarithmic curve a parabolic curve which has the 
same minimum point and the same radius of curvature 
at the minimum point as the original distribution. 
At twice the duct height the parabola has a standard 
slope, and it is continued from that point upward as 
a straight line of this slope (AB in Figure 1). 

The modification term is now represented entirely 

a By J. E. Freehafer, Radiation Laboratory, MIT. 


by the departure of the parabola from the line 
AB, i.e., 

M - M„ = t 10 5 6 


s[‘ + 5(3-')j- 0 S 3 S2 


M - M 0 = j 10 6 - % 
4 ad 


^2 


When the duct is low, the modes leak and are not 
far different from the standard ones. Thus it seems 



Figure 1 . Schematic M curve for ground-based duct. 


reasonable to employ the well-known methods of 
perturbation theory for calculating the characteristic 
values and functions of the parabolic atmosphere in 
terms of departures from standard. 

If we brush aside mathematical questions of a 
delicate nature, it is possible to obtain an approxi¬ 
mation for the characteristic values which leads to 
the following expression for the fractional change in 
the attenuation constant (i.e., the real part of y m ) 


R® ('Ym) R® (Ym) 

He (y m) 

f (f - 5) Im [hz 2 (f + e m )] d{ 

Jo 5 6 


5 [hz (e m )] 2 Im (e m ) 


315 


+ • 


Here, Re and Im designate the real and imaginary 
parts, and 


256 








ESTIMATION OF RADAR RANGES OVER THE OPEN OCEAN 


257 


5 = ^. 

L 

L is an abbreviation for (aX 2 / 67 r 2 )’ and is equal to 

33 ft for X = 10 cm, 

7m is the characteristic value for the standard case, 

7m is the characteristic value for the parabolic case, 

h{z) is (f**), 

Hi( 2) is the Hankel function of second kind, order 

34 of the argument ^z*^, 

e m ’s are roots of A 2 (f) = 0 . 

The expression above has been evaluated for the 
first mode by summing the series for A 2 and perform¬ 
ing the integration numerically. This curve is remark¬ 
able for the considerable interval in which the 
ordinate is practically zero. The attenuation constant 
differs by less than 1 per cent from the standard for 
ducts below 8 = 1 . 2 . Beyond this value the effect of 
the duct increases rapidly, and when 8 = 1.7 the 
attenuation constant is 10 per cent different from 
standard, and at 8 = 2 it is 20 per cent different. 

It seems that at least for radar purposes the 
condition 8 < 1 is a reasonable and convenient 
condition for defining a negligible duct. This is 
equivalent to saying that L /2 is the thickness below 
which a duct may for practical purposes be disre¬ 
garded. For instance, at X = 10 cm, L = 33 ft, and 
hence we conclude that the effect of ducts less than 
16 ft in thickness on 10 -cm radars may be neglected. 
On the other hand, if the wavelength is 3 m, L = 300 
ft, and ducts below 150 ft in thickness are negligible. 

If in the interest of simplicity we neglect the effect 
of small variations in the characteristic values on 
the characteristic functions, the fractional change in 
attenuation constant is also equal to the fractional 
change in the range against surface targets. It follows 
that the estimation of range can be reduced to a 
measurement of sea temperature and specific hu¬ 
midity at masthead level; for the duct thickness d 
under conditions of neutral equilibrium is given by 



q s is the saturation specific humidity at sea tempera¬ 
ture and q a the specific humidity at masthead. T is 
a parameter for which a representative value is 
0.08, and ( dq/dz) 0 is the gradient of specific humidity 
required to give zero M gradient under conditions 


of constant potential temperature. It is taken as 
H g per kg. 

Thus it turns out that 

5 = 0.32 gs ~ ^ 

Lj 

where ^ ^ a is in grams per kg per 100 ft . 

If L is given the appropriate value for X = 10 cm 
8 ^ q s - q a (g per kg) . 

For illustrative purposes, scales of ( q s — q a )/L and 
q s ~ q a for X = 10 cm have been added in Figure 2. 



Figure 2. Fractional drop in attenuation constant of 
the first mode versus duct thickness. Bottom scale for 
A q and A q/L corresponds to X = 10 cm. 


It is emphasized that the calculations are rough 
and are presented only in the belief that some sort 
of simple guiding principle may be more useful than 
a highly accurate and cumbersome formula. The 
results given are accurate out to variations in range 
of 1 per cent, and the determination of threshold 
thickness is completely reliable. Extension beyond 
8 = 1.2 is a definite extrapolation. The trend indi¬ 
cating that the increase in range goes up at least as 
fast as the sixth power of the duct thickness for 
5 > 1 is, we believe, real. 






















Chapter 27 

CONVERGENCE EFFECTS IN REFLECTIONS FROM 
TROPOSPHERIC LAYERS 4 


A n elevated duct may be treated as a concave 
spherical mirror whose radius of curvature is 
a, the effective earth radius. This includes any layer 
that can act as a reflector to radiation incident at a 
sufficiently small angle. The problem is here con¬ 
sidered as one of geometrical optics only. Ray tracing 
methods are used, and the phases are assumed to 
add randomly. This assumption may introduce an 
error as large as 3 db in the result but is necessary 
to simplify the solution of the problem. If the reflec¬ 
tion coefficient is other than unity, it must be 
multiplied into the general relation which will be 
given for C = KLM the net convergence factor. 

27 1 CONVERGENCE FACTOR 

A bundle of rays leaving a transmitter below the 
reflecting layer is converged on reflection from a 
concave surface. The convergence factor K is the 
ratio of the power density at the receiving antenna 
after convergence to the power density at the 
receiver that would be expected after reflection from 
a plane surface (essentially free space condition). 
Referring to Figure 1, the convergence factor can 
be expressed as 

K = O + y) 8d l 

x8d! + yb0 2 ’ K ) 

or 

K = ( 1 - 2xj/ ) ' , (2) 

\ ciR sin </>/ 

-- 2 -► 



where x = distance from transmitter to point of 
reflection, 

a By Ensign W. W. Carter, USNR Radio Division, Consult¬ 
ant Group. 


y = distance from receiver to point of reflec¬ 
tion, 

R = x + y = total range, 
a = effective earth’s radius (usually 4,590 
nautical miles), 

<fi = angle of incidence of radiation at reflec¬ 
tion, 

other angles as shown on Figure 1. 


Equation (2) can be deduced from equation (1) 
by remembering that 


and 


l = ada 


x8 fli 
sin 0 ’ 


(3) 


5 — 5 0 2 = 2 da 


2x8 0i 
a sin <f) ' 


The form shown in equation (2) is the more useful 
and is similar to the divergence factor for reflection 
at a convex surface that has been in use for some 
time. Equation (2) shows that K can grow quite 
large and even become infinite for certain conditions. 
Curve 1, Figure 2, shows a plot of the absolute value 


25 

21 

17 

13 
|K| 

9 

5 
1 

0 200 400 600 800 1000 1200 1400 ifiOO 1800 

b IN FEET-► 



Figure 2. Value of K for height of layer (6 in ft) versus 
range (nautical miles). 


of K as a function of b, the height of the layer above 
the antennas, for a total range of 80 nautical miles. 
This plot also assumes x = y — 40 miles, which is 
a necessary condition for a smooth reflector. In this 
case, K becomes infinite for a layer 1,100 ft above 
the antennas. Curve 2, Figure 2, shows a plot of 


258 






























CONCLUSIONS 


259 


the layer height b necessary to give infinite conver¬ 
gence as a function of the range (plotted on right- 
hand scale). 

272 ROUGHNESS EFFECT 

The most apparent difficulty with the picture 
presented so far is that the layers actually are not 
perfectly smooth. In order to take that fact into 
consideration, it was assumed that the layer was 
composed of a large number of plates set at various 
small angles about the horizontal according to a 
Gaussian distribution. As in other parts of this 
problem, variations are considered only in the plane 
of transmission, since the effect of sideways deviation 
would cancel out. This reduces the problem to one 
of two dimensions only. Each plate is further assumed 
to retain its original curvature. 

A beam falling on a patch of these plates would 
be reflected in such a way as to spread the energy 
at the receiver in a vertical pattern similar to the 
Gaussian distribution of the plates. It is only neces¬ 
sary to integrate this curve over the width of the 
antenna to find the fraction, L, of the- total energy 
that will be useful. L will be a function of the 
probable value of the deviation of the plates, the 
range, and the antenna width. 

With the rough layer assumption, there will be 
some plates correctly oriented at each part of the 
layer to reflect energy into the receiver. Therefore, 
a third factor, M, must be included that is the ratio 
of y/j8, where 7 is the total angle subtended by the 
layer that can reflect rays to the receiver. 7 would 
be limited by the optical horizons. /3 is the angle 
subtended by the receiving antenna when reflection 
is from a plane surface; i.e., essentially, free space 
conditions. 

The net convergence factor C must be the product 
of these three quantities K, L, M. In this case, K 


must be the mean value of K averaged for various 
points of reflection. In order to integrate the expres¬ 
sion for the mean value of K, it is necessary to substi¬ 
tute for sin <f> in equation (2). 


sin (f> — 

(b + ± + * + jO 

\x ^ 2a ^ y ^ 2a) ’ 

(5) 

which gives 




8 (xy) 2 T 1 

R 2 (2 ab + xy) J 

(6) 


This expression is easily integrated if the product 
xy is used for the variable and Xiyi = x\ (R — £1). 

Example. The preceding developments have been 
applied to the one-way link of the U. S. Navy Radio 
and Sound Laboratory at San Diego, which has been 
extensively studied. High subsidence layers are 
common for this region. The probable value of the 
deviation of a reflecting plate from horizontal was 
taken as 0.1° as an engineering approximation. In 
this case, C equals 43, assuming a reflection coeffici¬ 
ent of 1. If the reflection coefficient is not unity, its 
value as a function of angle of incidence must be 
multiplied into the equation. 

Since K, L, and M can each vary through con¬ 
siderable limits, C can vary through a very wide 
range of values. 

27 3 CONCLUSIONS 

The statistical treatment of the roughness is not 
always applicable, since a finite number of plates 
would actually be engaged in reflecting energy. 
Hence, the received signal would vary almost ran¬ 
domly with time as the orientation of the plates 
changed slightly. This could produce marked fading 
and peaks of large amplitude. Primarily, however, it 
would explain signals of the magnitude of free space 
signals or higher. 



























































. . - m 























































BIBLIOGRAPHY 

VOLUME I 


Numbers such as CP-100-M1 indicate that the document listed has been microfilmed and that its title appears in the microfilm 
index printed in a separate volume. For access to the index volume and to the microfilm, consult the Army or Navy agency 
listed on the reverse of the half-title page. 


1. Notes on Microwave Propagation Conference at MIT, 

Radiation Laboratory, Division 14 Report 42, RL, Sept. 
24, 1943. CP-100-M1 

2. International Radio Propagation Conference [held at Inter¬ 

service Radio Propagation Laboratory, from April 17 to 
May 5, 1944], Report IRPL-C61, National Bureau of 
Standards, June 1944. CP-100-M3 

3. Report of Second Propagation Conference, February 10 to 
11,1944 at the Empire State Building, New York, OEMsr- 
1207, NDRC CUDWR-WPG, February 1944. 

CP-100-M2 

4. Scientific Investigations on Propagation Problems in the 

Southwest Pacific Area, F.W.G. White, OSRD II-5- 
6124(S), ATP [Australian Radio Propagation Com¬ 
mittee], July 24, 1944. CP-110-M1 

5. The Air Defense System of the Near Islands, Thomas J. 

Carroll, Report 0 AD-55, U.S. Army Air Forces, Eleventh 
Air Force, OCSO, Operational Analysis Division, Aug. 
30, 1944. CP-202.1-M5 

6. Reviews of Progress of Ultra Short Wave Propagation 
Work, [USWPJ: 

6a. [Part] I, The Evaluation of Solutions of the Wave 
Equation for a Stratified Medium, D. R. Hartree, OSRD 
WA-2961-2, JEIA 5934, RDF 239, Report AC-7017, 
Sept. 26, 1944. CP-110-M2 

6b. [Part] II, Statement of Work in Progress Relevant to 
Investigations of the Propagation of Radio Waves Through 
the Troposphere, R. L. Smith-Rose, OSRD WA-3005-2, 
Report AC-7018, NPL, Sept. 25, 1944. CP-110-M3 

6c. [Part] III, Microwave Propagation Research at the 
Signals Research and Development Establishment, OSRD 
WA-3156-7, JEIA 6464, Report AC-7019, SRDE, Sept. 
26, 1944. CP-110-M4 

6d. [Part] IV, Correlation of Radar Operational Data with 
Meteorological Conditions, OSRD WA-3156-8, JEIA 6463, 
Report AC-7020, AORG, Sept. 28, 1944. CP-110-M5 

6e. [Part] V, Progress Report on Forecasting of Radar 
Conditions, OSRD WA-3156-9, JEIA 6462, Report 

AC-7021, DMO, Oct. 2, 1944. CP-110-M6 

6f. [Part] VI, Vertical Temperature and Humidity Gra¬ 
dients at Rye, OSRD WA-3156-10, JEIA 6461, Report 
AC-7022, DMO, Oct. 2, 1944. CP-110-M7 

6g. [Part] VII, The Use of Radar for the Detection of 
Storms, OSRD WA-3156-11, JEIA 6460, Report AC-7023, 
DMO, Oct. 2, 1944. CP-110-M8 

6h. [Part] VIII, Present States of Theoretical Study of 
Radio Propagation, Through the Troposphere by the Mathe¬ 
matics Group, TRE, OSRD WA-3156-12, JEIA 6459, Re¬ 
port AC-7024, TRE, Oct. 2, 1944. CP-110-M9 

6i. [Part] IX, Review of Short-Period Experimental Studies 
of Centimetre Wave Propagation, Carried Out Jointly by 


ASE, SRDE, and GEC, E. C. S. Megaw, OSRD WA- 

3156- 13, JEIA 6458, Report AC-7025, Oct. 16, 1944. 

CP-110-M10 

6j. [Part] X, Study of Centimetre Wave Propagation over 
Cardigan Bay to Mount Snowden, F. Hoyle, OSRD WA- 

3157- 1, Report AC-7026, Oct. 14, 1944.' CP-110-M11 

6k. [Part] XI, Study of Reflection Coefficient of the Sea at 
Centimetre Wavelengths, F. Hoyle, OSRD WA-3157-2, 
Report AC-7027, Oct. 14, 1944. CP-110-M12 

61. [Part] XII, Some K-, X-, and S-Band {Llandudno) 
Trials, General Summary of the Experimental Results Ob¬ 
tained which are Concerned with the Dependence of Radio 
Propagation on Meteorological Conditions, OSRD WA- 
3157-3, Report AC-7028, TRE and RRDE, Oct. 14,1944. 

CP-110-M13 

6m. [Part] XIII, Progress Report on 369 Trials by Di¬ 
rector, Naval Meteorological Service, OSRD WA-3156-1, 
JEIA 6466, RDF 240, Report AC-7029, Oct. 14, 1944. 

CP-110-M14 

6n. [Part] XIV, Survey of Progress in the United Kingdom 
on the Electromagnetic Theory of Tropospheric Propagation, 
OSRD WA-3157-4, Report AC-7030, RRDE, Oct. 16, 
1944. CP-110-M15 

6o. [Part] XV, Study of Meteorological Factors Responsible 
for the Refractive Structure of the Troposphere, OSRD WA- 
3157-5, Report AC-7031, RRDE, Oct. 16, 1944. 

CP-110-M16 

7. Report No. 1 of Project SWP-3.2 of the Office of Field 

Service, Paul A. Anderson and P. Squires, OEMsr-728, 
Research Project PDRC-647, Washington State College, 
Nov. 2, 1944. CP-335-M3 

8. Data on Super Refraction Supplied by Australian Radar 

Stations, J. W. Reed, Report RP-229/1, CSIR-RL, Dec. 
6, 1944. CP-223-M11 

9. Report No. 2 of Project SWP-3.2 of the Office of Field 

Service, Paul A. Anderson and P. Squires, OEMsr-728, 
Research Project PDRC-647, Washington State College, 
Jan. 7, 1945. CP-335-M3 

10. Third Conference on Propagation, Washington, D. C. [on] 
November 16 to 18, 1944, NDRC CUDWR-WPG, 1945. 

CP-100-M4 

11. Survey of Field of Radio Propagation and Noise with 

Special Reference to Australia, F. J. Kerr, OSRD II-5- 
6572(S), JEIA 8641, Report RP-231, CSIR, Nov. 27, 
1944. CP-110-M17 

12. Fourth Conference on Propagation, Washington, D. C. [on] 
May 7 [to] 8, 1945, NDRC CUDWR-WPG, 1945. 

13. Notes on Microwaves based upon a Series of Lectures by 
W. W. Hansen, Samuel Seely and Ernest C. Pollard, 
Division 14 Report T-2, RL, Oct. 20, 1941, Chaps. 1 to 3. 

CP-201.1-MI 


261 


262 


BIBLIOGRAPHY—VOLUME 1 


14. An Introduction to Microwave Propagation, Donald E. 

Kerr and Pearl J. Rubenstein, Division 14 Report 406, 
RL, Sept. 16, 1943. CP-201.1-M2 

15. Electrical Communication Systems Engineering, General 

Information, Technical Manual TM-11-486, U. S. War 
Department, Feb. 25, 1944. CP-204-M1 

Superseded by TM-11-486, Apr. 25, 1945 and Electrical 
Communication Systems Equipment, TM-11-487, Oct. 2, 
1944. 

16. Anomalous Propagation and the Army, Thomas J. Carroll, 
Report ORB-P-18-1, OCSO, Mar. 4, 1944. CP-221-M12 

17. Principles of Radar, Staff of MIT Radar School, June 15, 

1944. CP-202-M1 

18. Radar Performance Testing Manual, Manual 28, USAAF, 

Second Edition, July 1944. CP-202.31-MI 

19. Effects of Site Conditions on Operation of Ground Radar 

Installations on Aerodromes, J. L. Putnam, OSRD WA- 
4172-12, Report T-1805, TRE. CP-202.31-M2 

20. “The Diffraction of Electro-magnetic Waves from an 
Electrical Point Source Round a Finitely Conducting 
Sphere, with Applications to Radiotelegraphy and the 
Theory of the Rainbow,” H. Bremmer and Balth. Van 
Der Pol, The London, Edinburgh, and Dublin Philosophical 
Magazine and Journal of Science, 24, July 1937, Part I, 
pp. 141-176; Supplement, 24, November 1937, Part II, 
pp. 825-864; 25, June 1938, Part III, pp. 817-837; 27, 
March 1939, Part IV, pp. 261-275. 

21. Ultra Short Wave Propagation Curves, 0.1 to 10 Meters, 

OSRD WA-1502-la, Marconi Handbook, Marconi, Ltd., 
Mar. 28, 1940. CP-211-MI 

22. Report on Signal Strength Curves Within the Visual Range, 

OSRD WA-1463-1, Pamphlet RD-456, Marconi, Ltd., 
November 1940. CP-211-M2 

23. “The Effect of the Earth’s Curvature on Ground-Wave 

Propagation,” Chas. R. Burrows and Marion C. Gray, 
Proceedings of the Institute of Radio Engineers, 29, Jan¬ 
uary 1941, pp. 16-24. CP-231.12-M5 

24. “Ultra Short Wave Propagation,” I. C. Schelling, Chas. 
R. Burrows, and E. B. Ferrell, Proceedings of the Institute 
of Radio Engineers, 21, March 1933, pp. 427-463. (See 
reference 447.) 

25. Propagation Curves for Wavelengths of 18 Meters, Supple¬ 
ment to U. S. W. Propagation Curves RD-456, Appendix 
RD-456A, Marconi, Ltd., November 1941. (See refer¬ 
ence 22.) 

26. “The Calculation of Ground-Wave Field Intensity over a 
Finitely Conducting Spherical Earth,” K. A. Norton, 
Proceedings of the Institute of Radio Engineers, 29, Decem¬ 
ber 1941, pp. 623-639. 

27. Siting of Stations for Maximum Range, H. G. Booker, 
OSRD II-5-1183, Report M/36, TRE, Feb. 9, 1942. 

CP-231.11-M 2 

28. Microwave Interference Patterns, J. A. Stratton, Division 

14 Report C-l, RL, Mar. 7, 1942. CP-232.1-MI 

29. Theoretical Field Strength of Ten-Centimeter Equipment 
over a Spherical Earth, H. G. Booker, OSRD WA-210-3j, 
Report M/45/HGB, TRE, July 1, 1942. CP-231.12-MI 

30. Atmospheric Refraction and Height Determination by RDF, 


E. Eastwood, OSRD II-5-6511, JEIA 7773, Calibration 
Memorandum 54, RAF, July 6, 1942. (See reference 63.) 

CP-211-M3 

31. Dependence of Range of Submarine Radar Equipment on 
Wave Length, Case 20564, Chas. R. Burrows, Technical 
Memorandum MM-42-160-70, BTL, July 9, 1942. 

CP-212-M1 

32. Transmission on 3000 Me. over Sea Water, J. A. Stratton, 
Division 14 Report C-2, RL, July 14, 1942. CP-232.1-M2 

33. Transmission on 100 Me. over Sea Water, J. A. Stratton, 
Division 14 Report C-3, RL, July 14, 1942. 

CP-232.1-M3 

34. Transmission on 200 Me. over Sea Water, J. A. Stratton, 
Division 14 Report C-4, RL, July 14, 1942. 

CP-232.1-M4 

35. Transmission on 500 Me. over Sea Water, J. A. Stratton, 
Division 14 Report C-5, RL, July 14, 1942. 

CP-232.1-M5 

36. Interim Report on Propagation Within and Beyond the 
Optical Range, C. Domb and M. H. L. Pryce, Report 
M-448, ASE, September 1942. 

37. Theoretical Ground Ray Field Strengths and Height Gain 

Curves for Wavelengths of 2 to 2000 Megacycles, OSRD 
II-5-5274, Technical Report 383, Section E, BRL, Sep¬ 
tember 1942. CP-211-M4 

38. Siting for Long Range Aircraft Detection, Thomas J. 
Carroll, Technical Report T-13, CESL, Revised Oct. 17, 

1942. CP-202.11-MI 

39. V.H.F. Field Strength Curves for Propagation within the 
Line of Sight, G. J. Camfield, OSRD WA-570-3, Report 
Radio/279, Radio/s.2111/OPE 16, RAE, October 1942. 

CP-211-M5 

40. Relation of Radar Range to Frequency and Polarization, 

J. A. Stratton and Richard A. Hutner, Division 14 
Report C-6, RL, Nov. 3, 1942. CP-212-M2 

41. Propagation Curves [of] 1 to 10 Cm, G. Millington, OSRD 
WA-1502-lc, Report TR-460, Marconi, Ltd., January 

1943. CP-211-M6 

42. Properties of the Diffracted Wave Field Intensity, Richard 

A. Hutner and Elizabeth M. Lyman, Division 14 Report 
C-8, RL, Feb. 12, 1943. CP-233-M7 

43. The Effect of Earth Curvature on the Performance Diagram 
of an RDF Station, Report 29/R102/LGHH, TRE, Feb. 
25, 1943. 

44. Radar Height Finding, Richard A. Hutner, Helen Dod¬ 
son, Jocelyn Gill, Bernard Howard, Francis Parker, and 
J. A. Stratton, Division 14 Report C-9, RL, Apr. 6, 1943. 

CP-202.311-MI 

45. Technical Requirements of Ground Communications Inter¬ 
ceptor Search Systems, Technical Requirements for Early 
Warning Radar Systems, L. J. Chu and N. H. Frank, 
Division 14 Report TCAW-1 and -2, RL, May 10, 1943. 

CP-202.1-MI 

46. Low-Angle Coverage of Early Warning Radar Systems, N. 

H. Frank, Division 14 Report TCAW-3, RL, July 26, 
1943. CP-202.1-M2 

47. Factors Relating to the Design of an RDF Air Warning Set, 

F. J. Kerr, OSRD 11-5-5721, Report RP-187, CSIR-RL, 

Aug. 11, 1943. CP-202.1-M3 



BIBLIOGRAPHY—VOLUME 1 


263 


48. A Graphical Method of Computing the Bending of Radio 
Beams by the Effective Earth Radius Method, Harry Ray¬ 
mond, Technical Report T-14, CESL, Aug. 27, 1943. 

CP-231.12-M2 

49. Transmission at Low Altitudes over Sea Water, Richard 

A. Hutner, Francis Parker, Bernard Howard, Helen 
Dodson, and Jocelyn Gill, Division 14 Report C-10, RL, 
Sept. 1, 1943. CP-232.1-M6 

50. Radio-Frequency Propagation Above the Earth's Surface, 

Paul F. Godley, Jr., OEMsr-895, Division 15 Report 
895-5, RCA, Sept. 11, 1943. CP-231.12-M3 

51. Field Intensity Formulas, Richard A. Hutner, Helen Dod¬ 
son, Jocelyn Gill, Francis Parker, and Bernard Howard, 
Division 14 Report C-ll, RL, Sept. 28, 1943. 

Div. 14-111-M8 

52. Note on Field Intensity Computations for Elevated An¬ 

tennas, Case 20878, Marion C. Gray, OSRD WA-1463-23, 
Technical Memorandum MM-43-110-28, BTL, Oct. 9, 
1943. CP-211-M7 

53. The Calculation of Expected Vertical Coverage Diagrams 
by Max Sherman, February 19,1943, revised by Walter S. 
McAfee, Technical Report T-17, CESL, Oct. 15, 1943. 

CP-211-M8 

54. Charts for Use in Field Intensity Computations, K. Bull- 

ington, OEMsr-1018, Research Project C-79, NDRC 
Division 13 Preliminary Report 3460-KB-NF, Western 
Electric Company, Inc., Nov. 2, 1943. CP-211-M9 

55. Notes on Visibility Problems, Taking Account of the Cur¬ 

vature of the Earth, OSRD WA-1368-19, Report 152, 
AORG, Dec. 1, 1943. CP-231.12-M4 

56. Simplified Methods of Field Intensity Calculations in the 

Interference Region, William T. Fishback, Division 14 
Report 461, RL, Dec. 8, 1943. CP-211-M10 

57. Field Strength Near and Beyond the Horizon for Wave¬ 
lengths of Ten and Thirty Cms., M/Report 53/WW, 
TRE, Dec. 24, 1943. 

58. Theoretical Field Strength Near and Beyond Horizon for 
Orthodox Propagation of Fifty Centimeter Waves, OSRD 
WA-1976-5, Report T-1635/WW, TRE, Feb. 24, 1944. 

CP-211-M11 

59. The Propagation Functions for an Atmosphere with Uni¬ 
form Lapse-Rate of Refractive Index, T. Pearcey, OSRD 
WA-2985-1, Research Report 256, RRDE, Sept. 1, 1944. 

CP-211-M12 

60. Propagation Curves (third edition), NDRC Division 15 

Report 966-6C, October 1944. CP-211-M13 

61. Field Strength Calculator for Vertical Coverage Patterns 
and Propagation Curves, Clarence R. White, Technical 
Memorandum 154-E, CESL, Dec. 20, 1944. CP-211-M 14 

62. Theory of the Vertical Field Patterns for RDF Stations, 

J. C. Jaeger, OSRD II-5-4297, Report RP-174, CSIR-RL, 
Mar. 17, 1943. CP-213-M1 

63. Height, Range [and] Alpha Tables, Tables Relating to the 

Height, Range and Angle of Elevation of an Aircraft, OSRD 
II-5-6512, JEIA 7766, Radar Memorandum 50, ORS- 
ADGB, Aug. 10, 1944. (See reference 30.) CP-213-M2 

64. The Calculation of Field Strength for Vertical Polarization 

over Land and Sea on 20 to 80 Megacycles per Second, A. 
M. Woodward, OSRD WA-4395-11, Report T-1704, 
TRE. CP-211-M15 


65. Field Intensity Contours in Generalized Coordinates, Helen 
Dodson, Jocelyn Gill, and Bernard Howard, OEMsr-262, 
Division 14 Report 702, RL, May 2, 1945. CP-211-M 16 

66. The Limiting Ranges of RDF Sets over the Sea, F. Hoyle 

and M. H. L. Pryce, OSRD WA-1514-17, Report M-395, 
ASE, 1943. CP-232.2-M 2 

67. The Theory of Anomalous Propagation in the Troposphere 

and Its Relation to Waveguides and Diffraction, H. G. 
Booker, OSRD WA-599-10, Report T-1447, M/60/HGB, 
TRE, Apr. 12, 1943. CP-221-M2 

68. The Tracing of Rays in the Refracting Atmosphere, T. 

Pearcey, OSRD WA-645-42, Report AC-3878, ADRDE- 

USW, Apr. 21, 1943. CP-222-M2 

69. Graphical Construction of a Radar Radiation Pattern in a 

Stratified Atmosphere, Lloyd J. Anderson and F. R. 
Abbott, BuShips Problem X4-49CD, Report WP-4 [for 
the period from] March 1, 1943 to May 1, 1943, NRSL, 
May 1, 1943. CP-232.2-M3 

70. Improved Tropospheric Propagation, Curves Embracing 
Anomalous Propagation, H. G. Booker, OSRD II-5-4950, 
Report T-1482, M/65/HGB, TRE, July 6, 1943. 

CP-221-M3 

71. Radiation Patterns under Cases of Anomalous Propagation, 

T. Pearcey, OSRD WA-830-8, Report R-35/TP, 

ADRDE, July 19, 1943. CP-221-M5 

72. Effect of Humidity Gradients in the Atmosphere on Pro¬ 

pagation at RDF Frequencies, Operational Research Re¬ 
port 22, AORG, July 28, 1943. CP-222.1-M2 

73. The Calculation of Field Strength Near the Surface of the 

Earth under Particular Conditions of Anomalous Propa¬ 
gation, T. Pearcey, OSRD WA-931-6, Research Report 
203, ADRDE, Oct. 28, 1943. CP-221-M6 

74. Anomalous Propagation over the Earth, Case 23703, S. A. 

Schelkunoff, OSRD WA-1463-50, Report MM-43- 

110-33, BTL, Oct. 30, 1943. CP-221-M7 

75. The Effect of Atmospheric Refraction on Short Radio 

Waves, John E. Freehafer, Division 14 Report 447, RL, 
Nov. 29, 1943. CP-222-M5 

76. Radar Ray Patterns Associated with Normal and Anoma¬ 

lous Propagation Conditions, F. P. Dane, R. U. F. Hop¬ 
kins, and Lloyd J. Anderson, BuShips Problem X4-49CD 
Report WP-6 [for the period from] November 1 to De¬ 
cember 6, 1943, NRSL, Dec. 10, 1943. CP-221-M8 

77. Transmission of Plane Waves Through a Single Stratum 
Separating Two Media, John B. Smyth, BuShips Problem 
X4-49CD, Report WP-9, NRSL, Dec. 22, 1943. 

CP-221-M9 

78. Notes on Theoretical Coverage Diagrams for Anomalous 
Propagation, Donald E. Kerr, OSRD WA-1464-9, TM/ 
Memorandum/14/AMW, TRE, Jan. 1, 1944. 

CP-221-M 11 

79. The Dependence of Microwave Propagation over Sea on the 

Structure of the Atmosphere, J. M. C. Scott and T. Pearcey, 
OSRD WA-1591-9, Memorandum 40, ADRDE, Feb. 4, 
1944. CP-232.2-M 8 

80. Improved Tropospheric Propagation, Curves Embracing 
Superrefraction (revised edition), OSRD WA-1666-27, 
Report T-1625/WW, TRE, Feb. 18, 1944. 


CP-223-M1 



264 


BIBLIOGRAPHY—VOLUME 1 


81. TRE Requirements for Propagation, Curves Embracing 

Superrefraction, OSRD WA-1666-26, Report M/Memo- 
16/HAB, TRE, Feb. 25, 1944. CP-223-M2 

82. The Mechanical Determination of the Path Difference of 
Rays Subject to Discontinuities in the Vertical Gradient 
of Refractive Index, F. R. Abbott, BuShips Problem 
X4-49CD, Report WP-10, NRSL, Mar. 10, 1944. 

CP-222.1-M3 

83. Improved Tropospheric Propagation, Curves Embracing 

Superrefraction, OSRD WA-2026-2, Report T-1626/WW, 
TRE, Mar. 28, 1944. CP-223-M3 

84. Interservice Propagation, Curves Embracing Superrefrac¬ 

tion, Dependence of Mathematical Parameter L on Physical 
Entities, Report M/Memo-18/WW, TRE, Apr. 3, 1944. 

CP-223-M4 

85. Theoretical Coverage-Diagrams for 10 Cm. Radars Em¬ 

bracing Superrefraction, JEIA 3229, Report T-1634, 
TRE, Apr. 14, 1944. CP-223-M5 

86. Theoretical Coverage-Diagrams for 50 Cm. Radars Em¬ 

bracing Superrefraction, OSRD WA-1992-4, JEIA 3230, 
Report T-1659, TRE, Apr. 14, 1944. CP-223-M6 

87. Theoretical Coverage of Navigational Aids Embracing 

Superrefraction, OSRD WA-1992-6A, Report T-1660, 
TRE, Apr. 14, 1944. CP-223-M7 

88. The Theory of Propagation of Radio Waves in an Inhomo¬ 
geneous Atmosphere (Part I), T. Pearcey, OSRD WA- 
2251-5, Research Report 245, ADRDE, April 1944. 

CP-221-M10 

89. Reflection Coefficient of Layers of Varying Refractive Index, 

G. Millington, OSRD WA-2562-13, JEIA 4644, Report 
TR-483, BRL, April 1944. CP-222.1-M4 

90. Evaluation of the Solution of the Wave Equation for a 

Stratified Medium, D. R. Hartree, P. Nicholson, N. 
Eyres, J. Howlett, and T. Pearcey, OSRD WA-2341-4, 
Memorandum 47, ADRDE, May 24, 1944. (See reference 

108.) CP-221-M 13 

91. Transmission of Plane Waves Through a Single Stratum 

Separating Two Media (Part II), John B. Smyth, Bu¬ 
Ships Problem X4-49CD, Report WP-13, NRSL, June 
23, 1944. CP-221-M9 

92. Waves Guided by Dielectric Layers, S. A. Schelkunoff, Re¬ 
port MM-44-110-52, BTL, July 5, 1944. CP-221-M14 

93. Microwave Transmission in Nonhomogeneous Atmos¬ 

phere, S. A. Schelkunoff, Report MM-44-110-53, BTL, 
July 5, 1944. CP-221-M15 

94. Contour Diagrams of the Radiated Field of a Dipole under 
Various Conditions of Anomalous Propagation, T. Pear¬ 
cey and F. Whitehead, OSRD WA-2985-2, Research 
Report 257, RRDE, July 15, 1944. (See reference 110.) 

CP-221-M 16 

95. Theoretical Coverage-Diagrams for 1%-Meter Radars Em¬ 
bracing Super-refraction, A. M. W. Woodward, OSRD 
WA-2854-2, Report T-1708, TRE, July 23, 1944. 

CP-223-M9 

96. Propagation Curves Embracing Super-refraction: SS Duct, 

Profile-Index 0.2 (Preliminary Edition), H. G. Booker, 
M/Memo-23/WW, TRE, Sept. 7, 1944. CP-223-M10 

97. A Note on the Reflection Coefficient of an Isotropic Layer of 
Varying Refractive Index, G. Millington, OSRD WA- 
3172-1, JEIA 6481, Report TR-497, BRL, Oct. 5, 1944. 

CP-222.1-M5 


98. Predicted Low Level Coverage of S-Band Shipborne Radars 
as Affected by Weather, F. R. Abbott, L. L. Whittemore, 
L. W. Cross, and E. J. Wyrostek, BuShips Problem 
X4-49CD, Report WP-14, NRSL, Nov. 1, 1944. 

CP-232.2-M9 

99. Predicted Low Level Coverage of 200 MCS Band Shipborne 
Radars as Affected by Weather, F. R. Abbott, L. L. Whit¬ 
temore, L. W. Cross, and E. J. Wyrostek, BuShips Prob¬ 
lem X4-49CD, Report WP-15, NRSL, Nov. 4, 1944. 

CP-232.2-M10 

100. Variational Method for Determining Eigenvalues of Wave 
Equation of Anomalous Propagation, G. G. Macfarlane, 
Report T-1756, TRE, Nov. 13, 1944. 

101. Wave Propagation Analysis with the Aid of Non-Euclidian 

Spaces, Benjamin Liebowitz, OEMsr-1207, Report 
WPG-7, CUDWR, December 1944. CP-221-M18 

102. Atmospheric Waves, Fluctuations in High Frequency Radio 
Waves, L. G. Trolese and John B. Smyth, BuShips Prob¬ 
lem X4-49CD, Report WP-18, NRSL, Feb. 1, 1945. 

CP-225-M1 

103. The Relation Between the Wave Equation and the Non- 
Linear First Order Equation of the Riccati Type, T. L. 
Eckersley, OSRD WA-4223-7, JEIA 9104, Report TR- 
501, BRL, January 1945. (See reference 111.) 

CP-221.1-M 1 

104. A Report on Transmission of Waves over the Earth, T. L. 

Eckersley, OSRD WA-4002-13; Report TR-504, BRL, 
January 1945. CP-221.1-M2 

105. New Convergent Integrals, T. L. Eckersley, OSRD, WA- 
4002-11, Report TR-509, BRL, February 1945. 

CP-221.1-M3 

106. The Effect of a Subrefracting Layer of Atmosphere upon the 

Propagation of Radio Waves, T. Pearcey and M. Tomlin, 
OSRD WA-4016-28, JEIA 8371, Memorandum 83, 
RRDE, Feb. 12, 1945. CP-223-M13 

107. Theory of Characteristic Functions in Problems of Anoma¬ 

lous Propagation, W. H. Furry, OEMsr-262, Division 14 
Report 680, RL, Feb. 28, 1945. CP-221-M19 

108. The Evaluation of the Solution of the Wave Equation for a 

Stratified Medium ([Part] II), D. R. Hartree, OSRD 
WA-4424-11, Research Report 279, RRDE, Mar. 12, 
1945. (See reference 90.) CP-221-M20 

109. Theoretical Coverage Diagrams for 3-Meter Radars Em¬ 

bracing Super-refraction, W. Walkinshaw and R. Hens- 
man, OSRD WA-4320-7, JEIA 9198, Report T-1815, 
TRE, Mar. 18, 1945. CP-223-M12 

110. The Radiation Field of a Dipole under Various Conditions 

of Anomalous Propagation, T. Pearcey, M. Tomlin, and 
F. Whitehead, OSRD WA-4392-7, Research Report 275, 
RRDE, Apr. 13, 1945. (See reference 94.) CP-221-M21 

111. Notes on the Solution of a Non-Linear First Order Equation 

of the Riccati Type, T. L. Eckersley, OSRD WA-4428-7, 
JEIA 9725, Report TR-502, BRL, May 1945. (See refer¬ 
ence 103.) CP-222.1-M6 

112. Perturbation' Theory for an Exponential M-Curve in Non- 

Standard Propagation, C. L. Pekeris, OEMsr-1207, Re¬ 
port WPG-12, CUDWR, July 1945. CP-221.1-M4 

113. Graphs for Computing the Diffraction Field with Standard 

and Super standard Refraction, Pearl J. Rubenstein and 
William T. Fishback, OEMsr-262, Division 14, Report 
799, RL, Aug. 13, 1945. CP-222-M11 





BIBLIOGRAPHY —VOLUME 1 


265 


114. Radio Interpretation of Meteorological Observations in the 
First Two Meters of Atmosphere Above Grass at Harling- 
ton, Middlesex, January to June, 1940, OSRD WA-861-3, 
Report T-1471, M/63, TRE, June 1940. CP-222.1-MI 

115. Anomalous Echoes Observed with 10 Cm C.D. Set, A. E. 

Kempton, OSRD II-5-564, Research Report 119, 
ADRDE, Oct. 8, 1941. CP-623-M1 

116. Centimeter Wave Propagation over Sea Between High Sites 
just within Optical Range, F. Hoyle and E. C. S. Megaw, 
OSRD WA-171-12, ASE-GEC, June 12, 1942. 

CP-232.2-MI 

117. Centimeter Wave Propagation over Land {Part II), Meas¬ 
urements within and beyond Optical Range, G. W. N. 
Cobbold, H. Archer-Thomson, and E. C. S. Megaw, Re¬ 
port AC-2917, Com. 136, SRDE-GEC, Oct. 16, 1942. 

118. Radar Wave Propagation, Lloyd J. Anderson, John B. 
Smyth, F. R. Abbott, and R. Revelle, BuShips Problem 
X4-49CD, Report WP-2, NRSL, Nov. 30, 1942. 

CP-623-M2 

119. Very Short Wave Interception and D.F., T. L. Eckersley, 
OSRD II-5-5276, Report TR-438, BRL, 1943. 

CP-224-M2 

120. Anomalous Propagation of 10 Cm R.D.F. Waves over the 

Sea (February 6, 1943); First Supplement to Report 87 
(July 26, 1943), OSRD WA-909-21, Report 87, AORG, 
July 26, 1943. CP-232.2-M5 

121. Investigation of Propagation Characteristics of A.W. Sta¬ 
tions, Report 17, AORG, Mar. 9, 1943. CP-332-M1 

122. “A Study of Propagation over the Ultra-Short-Wave 
Radio Link between Guernsey and England on Wave¬ 
lengths of 5 and 8 Meters (60 and 37.5 Mc/s),” R. L. 
Smith-Rose and A. C. Stickland, The Journal of the In¬ 
stitution of Electrical Engineers, OSRD WA-1463-31, 
NPL, Vol. 90, No. 9, March 1943, Part III. CP-224-M3 

123. The Effect of Atmospheric Refraction on the Propagation of 

Radio Waves, A. C. Stickland, OSRD WA-623-19, Report 
RRB/S-10, NPL-RRB, Mar. 20, 1943. CP-222-M1 

124. Propagation of Ultra-Short Waves, H. C. Webster, OSRD 
II-5-4575(S), Report 354, Australia, Apr. 17, 1943. 

CP-224-M4 

125. Report on Radar Wave Propagation, Atmospheric Refrac¬ 

tion, A Qualitative Investigation, Lloyd J. Anderson and 
John B. Smyth, BuShips Problem X4-49CD, Report 
WP-5, NRSL, May 7, 1943. CP-222-M4 

126. Radio Interpretation of Meteorological Observations in the 
First 400 Feet Above Cardington, 1942, OSRD WA-861-1, 
Report T-1413, M/61, TRE, May 14, 1943. CP-321-M1 

127. Centimeter Wave Propagation over Sea {Part II), Measure¬ 
ments from Shore Sites Near and Beyond Optical Range, 
G. W. N. Cobbold, A. J. Jones, H. A. Bonnett, E. C. S. 
Megaw, H. Archer-Thomson, and E. M. Hickin, OSRD 
WA-792-10, Report 8180, GEC, May 27, 1943. 

CP-232.2-M4 

128. Preliminary Observations on Radio Propagation at 6 Centi¬ 

meters Between Beer’s Hill, New Jersey, and New York, 
Case 37003-4, File 36691-1, G. W. Gilman, Report 
MM-43-160-87, BTL, June 12, 1943. CP-224-M6 

129. Some Observations of Anomalous Propagation, Report 
T-1483, M/64, TRE, July 6, 1943. 


130. Application of Anomalous Propagation to Operational 
Problems at Hdme and Abroad, H. G. Booker, JMRP 3, 
Report T-1484, M/66/HGB, TRE, July 7, 1943. 

CP-221-M4 

131. Propagation of Signals on 45.1, 474 and 2800 Me from 

Empire State Building to Hauppauge and Riverhead, L.I., 
New York. G. S. Wickizer and A. M. Braaten, OEMsr- 
691, NDRC Research Project 423, Division 14 Report 
179, Report 1, RCA, July 20, 1943. CP-631-M1 

132. Propagation of Ultra Short Waves, T. L. Eckersley, OSRD 

WA-1463-3, Report TR/476, Marconi, Ltd., August 
1943. CP-224-M7 

133. The “K” Effect in Anomalous Propagation of Ultra-Short 
Waves, F. Syer (RAAF), JMRP 11, Australian Paper 
266, Report AC-4496, Australia, Aug. 10, 1943. 

CP-224-M15 

134. The Propagation of 10 Cm Waves over Land Paths of 14 , 
52, and 112 Miles, Paul A. Anderson, C. L. Barker, K. E. 
Fitzsimmons, and S. T. Stephenson, OEMsr-728, Re¬ 
search Project PDRC-647, Division 14 Report 202, 
Report 4, Washington State College, Oct. 26, 1943. 

CP-224-M8 

135. The Propagation of 1-Cm Waves over the Sea as Deduced 

from Meteorological Measurements, J. M. C. Scott and T. 
Pearcey, OSRD WA-1339-6, JMRP 4, Research Report 
227, ADRDE, Nov. 11, 1943. CP-232.2-M6 

136. Centimeter Wave Propagation over Land, A Preliminary 

Study of the Field.Strength Records between March and 
September 1943, R. L. Smith-Rose and A. C. Stickland, 
OSRD WA-1514-6, JMRP 10, Paper RRB/S-13, DSIR- 
NPL, Nov. 15, 1943. CP-333-M1 

137. The Propagation of 10 Cm Waves over an Inland Lake, 
Correlation with Meteorological Soundings, Paul A. Ander¬ 
son, K. E. Fitzsimmons, and S. T. Stephenson, OEMsr- 
728, Research Project PDRC-647, Division 14 Report 
212, Report 5, Washington State College, Nov. 12, 1943-. 

CP-232.2-M7 

138. Measurements of Radar Wave Refraction and Associated 
Meteorological Conditions, Lloyd J. Anderson and L. G. 
Trolese, Report WP-7, NRSL, Dec. 10, 1943. 

CP-222-M6 

139. Anomalous Propagation in India, Preliminary Report on 
Overland Transmission in Bengal, H. G. Booker, OSRD 
II-5-6555(S), Report S-5, ORS-SEA, Dec. 30, 1943. 

CP-334-M1 

140. Atmospheric Physics, Summary of Investigations on Anom¬ 

alous Propagation of Radar Signals Carried Out by the 
Australian Operational Research Group During 1942-43, 
D. F. Martyn, AORG, 1943. CP-221-M1 

141. The Cause of Short Period Fluctuations in CentimeterWave 
Communication, J. M. C. Scott, OSRD WA-1962-7 
Memorandum 42, ADRDE, Mar. 8, 1944. CP-224-M10 

142. Anomalous Propagation in the Persian Gulf, Naval Officer 

in Charge, Hormuz, OSRD WA-2146-23, Report AC- 
5975, USW, Received Mar. 20, 1944. CP-331-M4 

143. Effect of Super-refraction on Surface Coverage on Enemy 

50-Cm and 80-Cm Radar Sets, OSRD WA-2284-3, Report 
M/Memo-19 GGM, TRE, April 1944. CP-223-M8 

144. K-X-S Experiments, News Letter No. 1, T. Gold, MK. 

12201, ASE, May 3, 1944. CP-333.2-M1 




266 


BIBLIOGRAPHY—VOLUME 1 


145. Abnormal Radar Propagation in the South Pacific, An 

Investigation into Conditions in New Zealand and Nor¬ 
folk Island on 200 Mc/s. with Notes on Fiji, New Cale¬ 
donia and Solomon Islands, Air Department Wellington, 
File 135/14/10, Report 119, ORS-RNZAF, May 4, 
1944. CP-335-M1 

146. Procedure and Charts for Estimating the Low Level Cover¬ 

age of Shipborne 200-Mc Radars under Conditions of 
Pronounced Refraction, F. R. Abbott, Lloyd J. Anderson, 
F. P. Dane, J. P. Day, R. U. F. Hopkins, John B. 
Smyth, L. G. Trolese, and A. P. D. Stokes, BuShips 
Problem, X4-49CD, Report WP-11, NRSL, Revised 
May 10, 1944. CP-202.32-M1 

147. Centimeter Propagation over Land, A Study of the Field 
Strength Records Obtained During the Year 1943-1944, 
A. C. Stickland and R. W. Hatcher, JEIA 4789, Re¬ 
port RRB/S-18, NPL-MO, DSIR, May 11, 1944. 

CP-224-M11 

148. K-X-S Experiments, News Letter No. 2, T. Gold, MK. 

12201, ASE, May 13, 1944. CP-333.2-M1 

149. Atmospheric Propagation Effects and Relay Equipment, 

Thomas J. Carroll, Report ORB-PP-12-1, OCSO, May 
18, 1944. CP-311-M2 

150. Low-Level Coverage of Radars as Affected by Weather, 
Procedures and Charts, Report IRPL-T2a, NRSL, 
May 25, 1944. (Reference 146 reprinted.) 

151. Variations in Radar Coverage , Report JANP-101, Joint 

Communications Board, June 1, 1944. CP-202.4-M4 

Earlier edition: IRPL T-l, CUDWR-WPG, May, 
1944. CP-202.5-MI 

152. Effect of Atmospheric Refraction on Range Measure¬ 

ments, G. G. Macfarlane, OSRD I-A-320, Report T-1688, 
TRE, June 12, 1944. CP-222-M7 

153. Microwave Transmission over Water and Land under 
Various Meteorological Conditions, Pearl J. Rubenstein, 
I. Katz, L. J. Neelands, and R. M. Mitchell, OEMsr- 
262, Division 14 Report 547, RL, June 13, 1944. 

CP-311-M4 

154. Abnormal Propagation in W. A. C. for May and June, 
1944 • Report 10, Canadian ORS-WAC, July 27, 1944. 

155. Propagation of Signals on 45.1, 474 and 2800 Me from 
Empire State Building, N.Y.C. to Hauppauge and 
Riverhead, L.I ., N.Y., G. S. Wickizer and A. M. Braaten, 
OEMsr-691, NDRC, Research Project 423, Division 14 
Report 298, Report 2, RCA, July 31, 1944. CP-631-M1 

156. The Structure of the Electromagnetic Field During Con¬ 

ditions of Anomalous Propagation, T. Pearcey and F. 
Whitehead, OSRD WA-3070-1, Research Report 258, 
RRDE, Sept. 19, 1944. CP-221-M17 

157. Tropospheric Propagation and Radio-Meteorology, Re¬ 
port WPG-5, CUDWR-WPG, September 1944. 

158. “Some Factors Causing Super-refraction on Ultra High 
Frequencies on South West Pacific,” (Daily Report on 
Abnormal Echoes, RAAF Form 146 included in ATP 
821), D. F. Martyn and P. Squires, Australian Iono¬ 
sphere Bulletin, October 1944, Section 1.2. CP-224-M14 

159. Atmospheric Refraction, A Preliminary Qualitative Inves¬ 

tigation, Lloyd J. Anderson, F. P. Dane, J. P. Day, 
R. U. F. Hopkins, L. G. Trolese, and A. P. D. Stokes, 
BuShips Problem X4-49CD, Report WP-17, NRSL, 
Dec. 28, 1944. CP-222-M9 


160. Anomalous Propagation with High and Low Sited 3 Cm 
Ship Watching Radar Sets, G. C. Varley, OSRD WA- 
4238-2, Report 250, AORG, Mar. 20, 1945. 

CP-232.2-M12 

161. Anomalous Propagation at English Coastal Radar Sta¬ 

tions, March to September, 1944, L>. Lack, OSRD WA- 
4491-12, JEIA 9946, Report 258, AORG, May 30, 1945. 
(See also reference 6d.) CP-232.2-M13 

162. Lebanon-Beer’s Hill Transmission on Wavelengths of 2.0 
Meters, and 30 Centimeters, Case 20564, A. B. Crawford, 
Report MM-39-326-98, BTL, Dec. 5, 1939. CP-224-M1 

163. Centimeter Wave Propagation over Land; Preliminary 
Trials, G. W. N. Cobbold, H. A. Bonnett, A. J. Jones, 
E. C. S. Megaw, H. Archer-Thomson, A. S. Gladwin, 
and E. M. Hickin, Report 8045, GEC, Aug. 21, 1942. 

164. The Propagation of 10-Cm Waves on a 52-Mile Optical 

Path over Land, The Correlation of Signal Patterns and 
Radiosonde Data, Paul A. Anderson, C. L. Barker, S. T. 
Stephenson, and K. E. Fitzsimmons, OEMsr-728, 
NDRC Research Project PDRC-647, Division 14 
Report 151, Report 1, Washington State College, June 
10, 1943. CP-224-M5 

165. Centimeter Wave Propagation over Sea Within and Be¬ 
yond the Optical Range, E. C. S. Megaw, H. Archer- 
Thomson, E. M. Hickin, and F. Hoyle, Report M-532, 
ASE, July 1943. 

166. Aden-Berbera V.H.F. Experiments, Final Report on 

Propagation Aspects, E. W. Walker and S. R. Bicker- 
dike, OSRD WA-2187-14, Report MS-4, SRDE, De¬ 
cember 1942 and July 1943. CP-331-MI 

167. [Ultra Short Wave Communication ], Investigation No. 369, 

Irish Sea Experiment, OSRD WA-2146-18, -19, -20, -21, 
and -22; WA-2379-2, WA-2797-36, WA-3158-13; WA- 
3822-30; and -31. Or, as identified in Progress Reports 
AC-5970 Sept. 1, 1943, AC-5971 Dec. 14, 1943, AC- 
5972 Jan. 15, 1944, AC-5973 Feb. 9, 1944, AC-5974 
Mar. 20, 1944, AC-6334 May 14, 1944, AC-6828 Aug. 
12, 1944, AC-7206 Oct. 19, 1944, AC-7465 Nov. 10, 
1944, and AC-7668 Jan. 4, 1945, British Ministry of 
Supply. CP-224-M9 

168. Experience with Space and Frequency Diversity Fading 

on New York-Neshanic Microwave Circuit, Case 37003-4, 
G. W. Gilman and F. H. Willis, Report MM-43-160- 
152, BTL, Sept. 18, 1943. CP-240-M1 

169. Investigation of Changes in Direction of Transmission 

during Periods of Fading in the Microwave Range, Case 
37003-4, File 36691-1, A. C. Peterson, Report MM-43- 
160-183, BTL, Oct. 30, 1943. CP-240-M2 

170. Radar Calibration Report, New York “Region, R. C. L- 
Timpson, Mitchell Field, N.Y., Nov. 30, 1943. 

CP-202.1-M4 

171. Aden-Berbera VIIF Experiments, Meteorological Com 

ditions and Possible Correlations, E. W. Walker, OSRD 
WA-1614-1, JMRP 14, Report AC-5493, USW-SRDE, 
Dec. 20, 1943. CP-331-M3 

172. Propagation over Short Paths and Rough Terrain at 200 
Mc/s, A. B. Vane and D. G. Wilson, OEMsr-262, Di¬ 
vision 14 Report 468, RL, Jan. 18, 1944. CP-231.2-M 1 

173. Propagation and Reflection Characteristics of Radio 
Waves as Affecting Radar, William G. Michels and 





BIBLIOGRAPHY—VOLUME 1 


267 


William C. Pomeroy, Service Project (M-3) 11a, U.S. 
Army Air Forces Board, Jan. 31, 1944. CP-531-M1 

174. Microwave Propagation Measurements (Conference of 
February, 1944), F. H. Willis, Report MM-44-160-55, 
BTL, Mar. 10, 1944. (See reference 3.) 

175. An Estimation of the Incidence of Anomalous Propa¬ 

gation in the Cook Strait Area of New Zealand from Jan¬ 
uary 194S to January 1944, F. E. S. Alexander, OSRD 
II-5-5849(S), Report RD-1/373, RDL-DSIR, NZ, May 
2, 1944. CP-332-M2 

176. K-Band Radar Transmission, A Preliminary Report of 

Tests Made Near Atlantic Highlands, N.J. between 'De¬ 
cember 1943 and April 1944, G. C. Southworth, A. P. 
King, and S. D. Robertson, Report MM-44-160-115, 
BTL, May 19, 1944. CP-202.2-M1 

177. Report on Cross Channel Propagation of British No. 10 

Set, K. R. Spangenberg, Report OAB-2, OCSO, Aug. 
26, 1944. CP-224-M12 

178. Radar Range and Signal Strength, L. Jofey and A. C. 
Cossor, Report MR-142, Research Department, Myra 
Works, London E10, August 1944. 

179. Results of Microwave Propagation, Tests on the New 
York-Neshanic Path, Case 37003-4, File 36691-1, A. L. 
Durkee, Report MM-44-160-190, BTL, Aug. 28, 1944. 

CP-224-M13 

180. Height-Gain Tests in the Troposphere, G. A. Isted, JEIA 

5560, JMRP 36, Report TR-488, BRL, September, 
1944. CP-312-M1 

181. Interim Report on Investigation of 120 Mc/s and 50-Cm 

Propagation Across the English Channel, W. R. Piggott, 
OSRD WA-3157-6, Report AC-7081, USW, Oct. 4, 
1944. CP-333-M5 

182. Measurements of the Angle of Arrival of Microwaves in 
the X-Band, Case 20564, W. M. Sharpless, Report MM- 
44-160-249, BTL, Nov. 7, 1944. 

183. Over water Transmission Measurements, 1944-Dwrl /: 

Preliminary Analysis of Radio and Radar Measure¬ 
ments, Pearl J. Rubenstein, OEMsr-262, Division 14 
Report 649, RL, Dec. 15, 1944. CP-222-M8 

184. The Vertical Distribution of Field Strength over the Sea 
Under Conditions of Normal and Anomalous Propa¬ 
gation, J A Ramsay and P. B. Blow, OSRD WA-3870-1, 
Research Report 267, CAEE-RRDE, Jan. 5, 1945. 

CP-232-M1 

185. Centimetre Wave Propagation over Sea, A Study of 
Signal Strength Records Taken in Cardigan Bay, Wales 
Between February and September, 1944, R- L. Smith- 
Rose and A. C. Stickland, OSRD WA-4297-9, JMRP 
50, Paper RRB/C-114, NPL-DSIR, Feb. 28, 1945. 

CP-333-M3 

186. Over-Water Tests of S-Band Early Warning for Ships, 

Vertical Coverage of the CXHR (SCI) Search System, 
Walter O. Gordey, Donald T. Drake, and M. Kessler, 
OEMsr-262, Service Project NS-194, Division 14 Re¬ 
port 703, RL, Mar. 5, 1945. CP-232.2-M11 

187. Preliminary Report on S- and X- Band Propagation in 
Low Ducts Formed in Oceanic Air, Martin Katzin, Prob¬ 
lem S411.2R-S, Report R-2493, NRL, Mar. 24, 1945. 

CP-222.2-M2 


188. Atmospheric Refraction under Conditions of a Radiation 

Inversion, Llbyd J. Anderson, J. P. Day, C. H. Freres, 
R. U. F. Hopkins, John B. Smyth, and A. P. D. Stokes, 
BuShips Problem X4-49CD, Report WP-19, NRSL, 
Apr. 21, 1945. CP-222-M10 

189. Radio-Meteorological Relationships, E. C. S. Megaw and 

F. L. Westwater, OSRD WA-4594-15, Report AC-8140, 
USW-138, May 4, 1945. CP-222.2-M3 

190. Calculated Relationship Between Signal Level and Uni¬ 
form Gradient of Refractive Index for the Irish Sea Paths, 
E. C. S. Megaw, OSRD WA-4594-13, GEC Report 8656, 
AC-8225, USW-141, GEC-USW, Apr. 19, 1945. 

CP-222.1-M8 

191. Radio-Meteorological Relationships, General Summary of 

Papers AC- 8 I 4 O/USW.138 and AC-8225/USW.141, E. 
C. S. Megaw and F. L. Westwater, OSRD WA-4618-1, 
Report AC-8336, USW-149, USW, 1945. (See references 
189 and 190.) CP-222.2-M4 

192. General Summary Covering the Work of the KXS Inter- 

Service Trials, Llandudno, 1944, J- R. Atkinson, JMRP 
64, Report T-1770, TRE, May 1945. CP-333.2-M2 

193. X-Band Trials at Rosehearty, J. R. Atkinson, OSRD 

WA-4596-11, JEIA 10401, Report AC-8228, USW-142, 
May 28, 1945. CP-222.3-M1 

194. S- and X- Band Propagation in Low Ocean Ducts (Fourth 
Conference), R. W. Bauchman and W. Binnian, Report 
R-2565, NRL, July 5, 1945. (See reference 12 and 187.) 

195. KXS Llandudno Interservice Trials, Summer 1944, 
JMRP 68, Report T-1865, TRE, 1944. 

196. Survey of Radio Meteorological Information Available at 
TRE, JMRP 67, Report M/98 (T-1888)/JWH, TRE, 
August 1945. 

197. The Diffusive Properties of the Lower Atmosphere, O. G. 
Sutton, OSRD WA-670-9a, Report MRP-59, Chemical 
Defense Experimental Station, Air Ministry Meteoro¬ 
logical Research Committee, Dec. 29, 1942. CP-323-M1 

198. A Study of the Effect of the Meteorology on the Refraction 

of Radio Beams, H. Raymond, Technical Report T-2, 
CESL, May 4, 1943. ‘ CP-222-M3 

199. The Rapid Reduction of Meteorological Data to Index of 
Refraction, Lloyd J. Anderson and F. R. Abbott, Report 
WP-8, NRSL, Dec. 10, 1943. 

200. Application of Diffusion Theory to Radio Refraction 
Caused by Advection, P. M. Woodward, OSRD, WA- 
2047-4, Report T-1647, TRE, Apr. 6, 1944. CP-323-M2 

201. Qualitative Survey of Meteorological Factors Affecting 
Microwave Propagation, I. Katz and J. M. Austin, 
OEMsr-262, Division 14 Report 488, RL, June 1, 1944. 

CP-311-M3 

202. The Influence of Ground Contour on Air Flow (Trans¬ 

lation), P. Queney, Translated by Walter M. Elsasser, 
OEMsr-1207, Report WPG-4, CUDWR, September 
1944. CP-322-M1 

203. Radio-Meteorological Tables, P. M. Woodward and J. 

W. Head, OSRD WA-3401-1, JMRP 30, Report T-1724, 
TRE. CP-222.1-M9 

204. Modified Index Distribution Close to the Ocean Surface, 
R. B. Montgomery and Robert H. Burgoyne, OEMsr- 
262, Division 14 Report 651, RL, Feb. 16, 1945. 

CP-222.2-MI 



268 


BIBLIOGRAPHY — VOLUME 1 


205. Tables for Computing the Modified Index of Refraction 
M, E. R. Wicher, Report WPG-8, CUDWR, March 
1945. 

206. Nomograms for Computation of Modified Index of Refrac¬ 

tion, Robert H. Burgoyne, OEMsr-262, Division 14 Re¬ 
port 551, RL, Apr. 6, 1945. CP-222.1-M7 

207. Meteorological Report in Connection with V.H.F. Wireless 

Experiment Between Aden and Berber a, 1943, Ronald 
Frith, OSRD WA-1746-2, JMRP 13, Report AC-5492, 
USW, Oct, 30, 1943. CP-331-M2 

208. Meteorological Measurements, Irish Sea Experiments: 

Meteorological Observations [taken] on [Board] the Ship 
Glen Strathallan in the Irish Sea for the Period November 1, 
1943 to October 23,1944, OSRD WA-1759-14, WA-1935-1, 
WA-1951-1, WA-2131-5, WA-2131-C5, WA-2152-13, 
WA-2131-5A, WA-3180-1, WA-2242-4, WA-2315-1, 

WA-2364-13, WA-2587-5, WA-2623-13, WA-2843-13, 
WA-4079-1, WA-2905-4, WA-3029-2, WA-3180-1A, WA- 
3180-1D, WA-3322-1, and WA-3584-3, NMS. 

CP-333.1-MI 

Meteorological Observations [taken] on [Board] the Ship 
Coila in the Irish Sea for the Period December 15, 1943 to 
October 26, 1944, OSRD WA-2131-5B, WA-2843-11, 
WA-2743-12, WA-4079-2, WA-3305-5, WA-3322-2, and 
WA-3584-2, NMS. CP-333.1-M2 

Meteorological Measurements [taken] on [Board] the Ship 
St. Dominica in the Irish Sea for the Period May 19, 1944 
to August 29, 1944, OSRD WA-2587-6, WA-2645-4, WA- 
3143-9, WA-3991-2, WA-3180-1B, and WA-3180-1C, 
Inter-Service Cm. Wave Prop. Research NMS. 

CP-333.1-M3 

209. Tables of Temperature and Humidity Observations at Rye, 

OSRD WA-1463-13A, Report JMRP-5, MO, November 
1943. CP-333.3-MI 

210. Low Altitude Measurements in New England to Determine 
Refractive Index, 1943, Robert H. Burgoyne and I. Katz, 
Division 14 Report 42, RL, Feb. 22, 1944. CP-336.2-MI 

211. Climate in Relation to Microwave Radar Propagation in 

Panama, Arthur E. Bent, Division 14, Report 476, RL, 
Feb. 25, 1944. CP-336.1-MI 

212. The Vertical Distribution of Temperature and Humidity at 

Rye on the Night of January 14-15, 1944, JEIA 10318, 
Report JMRP 6, MO, Feb. 26, 1944. CP-333.3-M2 

213. Analysis of Temperature and Humidity Records at Rye, 
JEIA 10319, Report JMRP-7, MO, February 1944. 

CP-333.3-M3 

214. Radio Climatology of the Persian Gulf and Gulf of Oman 

with Radar Confirmation, H. G. Booker, Report T-1642, 
TRE, Mar. 15, 1944. CP-331-M5 

215. Stations in the Western Hemisphere with Conditions in the 
Lower Layers of the Atmosphere Similar to Those at 
Selected Stations in the Eastern Hemisphere, Report 729, 
U.S. Army Air Forces, Weather Division, March 1944. 

CP-337-M1 

216. Some Values of the Refractive Index of the Atmosphere at 
Rye, S. 100958, JEIA 10322, Report JMRP 23, MO 8, 
June 1-6, 1944. 

217. Low-Level Meteorological Soundings and Radar Correla¬ 
tion for the Panama Canal Zone, K. E. Fitzsimmons, S. T. 
Stephenson, and Robert W. Bauchman, OEMsr-728, 


NDRC Research Project PDRC-647, Report 6, Wash¬ 
ington State College, June 12, 1944. CP-336.1-M2 

218. Wave Propagation Report No. 3, Report 413.44/R113, 
Naval Research Group, Intel. Br. OCSO Canal Zone, 
July 1, 1944. 

219. Preliminary Analysis of Height-Gain Tests in the Tropo¬ 
sphere, R. F. C. McDowell, OSRD WA-2930-2, JEIA 
5777, Report TR-494, BRL, September 1944. 

CP-333-M2 

220. Diurnal Variation of Temperature and Humidity at Var¬ 

ious Heights at Rye, S. 100958, JEIA 10323, Report 
JMRP 26, MO 8, Oct. 21, 1944. CP-333.3-M4 

221. Report on General Climatic and Meteorological Conditions 

in Banda Sea, 4°-7° S., 126°-131° E., Report List 2, Sec¬ 
tion II, Series 7, No. 18, RAAF, Directorate of Meteoro¬ 
logical Services, November 1944. CP-335-M2 

222. Hourly Values of Modified Refractive Index M for Meteoro¬ 

logical Office [at] Rye, May, 1944, JEIA 10325, Report 
JMRP-31, MO, Dec. 28, 1944. CP-333.3-M5 

223. Temperature and Humidity Measurements Made with the 

Washington State College Wired Sonde Equipment at Kai- 
koura, New Zealand, Between Sept. 22, 1944 an d Oct. 19, 
1944, F. E. S. Alexander, Report RD-1/482, RDL-DSIR, 
NZ, Jan. 15, 1945. CP-332-M3 

224. Highlights of the December, 1944 Typhoon Including 

Photographic Radar Observations (Part I), A Distant Ob¬ 
servation of a Warm Front Including a Photograph of 
Cloud Forms and Slope of Front (Part II), George F. 
Kosco, Fleet Weather Central Paper 10, U.S. Navy, 
Third Fleet, Feb. 10, 1944. CP-336.3-M1 

225. Results of Low Level Atmospheric Soundings in the South¬ 
west and Central Pacific Oceanic Areas, Paul A. Anderson, 
K. E. Fitzsimmons, G. M. Grover, and S. T. Stephenson, 
OEMsr-728, NDRC Research Project PDRC-647, Re¬ 
port 9, Washington State College, Feb. 27, 1945. 

CP-335-M4 

226. Centimeter Wave Propagation over Sea, Correlation of 

Radio Field Strength Transmitted Across Cardigan Bay, 
Wales with Gradient of Refractive Index Obtained from Air¬ 
craft Observations, R. L. Smith-Rose and A. C. Stickland, 
OSRD WA-4459-9, JEIA 9813, Paper RRB/C-121, 
DSIR, May 10, 1945. CP-333-M4 

227. Balloon Psychrometer for the Measurement of the Relative 

Humidity of the Atmosphere at Various Heights (and Ad¬ 
dendum), S. M. Doble and S. Inglefield, OSRD II-5- 
5079(S) and OSRD II-5-5080(S), ICI, Apr. 1, 1943; 
Addendum Sept. 25, 1943. CP-344-M1 

228. The Captive Radiosonde and Wired Sonde Techniques for 

Detailed Low-Level Meteorological Sounding, Paul A. 
Anderson, C. L. Barker, K. E. Fitzsimmons, and S. T. 
Stephenson, OEMsr-728, NDRC Research Project 
PDRC-647, Division 14 Report 192, Report 3, Washing¬ 
ton State College, Oct. 4, 1943. CP-341-M1 

229. Instruments and Methods for Measuring Temperature and 

Humidity in the Lower Atmosphere, I. Katz, OEMsr-262, 
Service Project SC-8, Division 14 Report 487, RL, Apr. 
12, 1944. CP-344-M2 

230. Anomalous Propagation, Adaptation of Model RAU-2 
Radio Sonde Receiving and Recording Equipment for Use 
as Low Level Sounding Device, Navy Dev. Project Unit 1, 



BIBLIOGRAPHY—VOLUME 1 


269 


Friez Instrument Division, Bendix Aviation Corpora¬ 
tion, May 31, 1944. CP-342-M1 

231. Meteorological Investigation at Rye, Instrumental Lay¬ 

out for Recording Gradients of Temperature and Relative 
Humidity {Part I), Report JMRP-17, Instruments 
Branch, MO 4, May 1944. CP-344-M3 

232. Notes on Operational Use of Low-Level Meteorological 

Sounding Equipment, K. E. Fitzsimmons, S. T. Stephen¬ 
son, and Robert W. Bauchman, OEMsr-728, NDRC 
Research Project PDRC-647, Report 7, Washington 
State College, June 15, 1944. CP-342-M2 

233. Microwave Propagation Studies, Detection of Tropo¬ 
sphere Stratification by Means of Sound Echoes, Pre¬ 
liminary Trial, Case 87003, H. B. Coxhead and F. H. 
Willis, Report MM-44-160-143, BTL, June 21, 1944. 

CP-344-M4 

234. Operating Instructions for the WSC Low-Level Atmos¬ 
pheric Sounding Equipment, Paul A. Anderson, OEMsr- 
728, NDRC Research Project PDRC-647, Report 8, 
Washington State College, July 10, 1944. CP-342-M3 

235. Meteorological Equipment for Short Wave Propagation 
Studies, Walter M. Elsasser, Report WPG-3, CUDWR 
August 1944. 

236. Wired Sonde Equipment for High Altitude Soundings, 
Lloyd J. Anderson, BuShips Problem X4-49CD, Re¬ 
port WP-16, NRSL, Nov. 17, 1944. (See reference 238.) 

CP-341-M2 

237. A Note on the Resistance of Electric Hygrometer Ele¬ 

ments, Lloyd J. Anderson and S. T. Stephenson, Report 
AERO-1, NRSL, May 8, 1945. CP-343-M1 

238. Improvements in USNRSL Meteorological Sounding 
Equipment, Lloyd J. Anderson, S. T. Stephenson, and 
A. P. D. Stokes, BuShips Problem X4-49CD, Report 
WP-21, NRSL, July 3, 1945. (See reference 236.) 

CP-341-M3 

239. Forecasting of R. D. F. Conditions, JMRP 2, Memoran¬ 
dum 103, AORG, May 31, 1943. CP-410-M1 

240. The Meteorological Aspects of Anomalous Propagation, 

Short Wave Radio, R. W. Hatcher, Report JMRP 1, 
[Great Britain] June 1943. CP-410-M2 

241. Oboe Propagation, August-0ctober, 1943, H. G. Booker, 
OSRD WA-1464-5, Report T-1605, TRE, 1943. 

CP-422-M1 

242. “Naviprop” Forecasts, E. Gold, OSRD WA-2255-1Q, 

Report SIS 45, MO, Nov. 8, 1943. CP-422-M2 

243. Issue of Anoprop Forecasts , Synoptic Instruction Special 

No. 39, OSRD WA-2255-1R, Report SIS 39, MO, Feb. 
11, 1944. CP-422-M3 

244. Elements of Radio Meteorological Forecasting, H. G. 

Booker, Report T-1621, Mathematics Group, TRE, 
Malvern, Feb. 14, 1944. CP-410-M3 

245. Preliminary Instruction Manual, Weather Forecasting 

for Radar Operations, Report 614, U. S. Army Air Forces, 
Weather Division, March 1944. CP-410-M4 

246. Tropospheric Weather Factors Likely to Affect Superre¬ 

fraction of VHF-SHF Radio Propagation as Applied to 
the Tropical West Pacific, E. Dillon Smith and R. D. 
Fletcher, Report RP-1, U. S. Department of Commerce, 
Weather Bureau, July 1,1944. CP-424-M1 


247. Preliminary Instruction Manual of Weather Forecast¬ 

ing for Radar Operations in South West Pacific Area, 
D. F. Martyn and P. Squires, Report RP-220, CSIR- 
RL, Sept. 4, 1944. CP-424-M2 

248. Outline of Radio Climatology in India and Vicinity, 

H. G. Booker, JEIA 6061, Report JMRP-25, Report 
T-1727 (M/85), TRE, Sept. 12, 1944. CP-423-M1 

249. Notes on TRE Report T-1727, JMRP No. 25, Radio 

Climatology in India and Vicinity, C. S. Durst, JEIA 
10324, Report JMRP-27, MO, Nov. 7, 1944. (See refer¬ 
ence 248.) CP-423-M2 

250. A Rough Sketch of World Radio Climatology over Sea, 
H. G. Booker, Report T-1730, TRE, Oct. 31, 1944. 

CP-424-M3 

251. American Continents Meteorological Counterparts of 
Western Pacific and Indian Ocean Areas as Applied to 
Tropospheric Radio Propagation, J. H. Brown, J. L. 
Paulhus, and E. Dillon Smith, Report RP-2, U. S. 
Weather Bureau, Nov. 15, 1944. 

252. The Possibility of Investigating the Fohn Wind and Sea 

Breeze Phenomena in N. Z. with a View to Elucidating 
Certain Problems of Radio-Meteorological Forecasting in 
Other Parts of the World, M. A. F. Barnett and F. E. S. 
Alexander, JEIA 7469, Report RD-1/471, RDL-DSIR- 
NZ, Dec. 1, 1944. CP-421-M1 

253. Determination of a Suitable Method of Forecasting Radar 

Propagation Variations over Water, Tests Conducted by 
26lh Weather Region, Orlando, Florida, J. R. Gerhardt 
and William E. Gordon, Service Project 4252R000.77, 
U. S. Army Air Forces, Mar. 10, 1945. CP-425-M1 

254. A Qualitative Outline of the Radio Climatology of Aus¬ 

tralasia, H. G. Booker, JMRP-53, Report T-1820 
(M/95), TRE, Apr. 19, 1945. CP-421-M2 

255. Determination of the Practicability of Forecasting Me¬ 
teorological Effects on Radar Propagation, Tests Con¬ 
ducted by AAF Tactical Center, Orlando, Florida, John 
R. Gerhardt and William E. Gordon, Service Project 
3767B000.93, U. S. Army Air Forces, June 13, 1945. 

CP-425-M2 

256. Absorption of 1-Cm Radiation by Rain, M. G. Adam, 
R. A. Hull, and C. Hurst, Misc. Report 3, CVD-CL. 

257. The Absorption of Ultra-Short Wireless Waves in the 

Water Vapour of the Earth’s Atmosphere, J. A. Saxton, 
OSRD II-5-210, Paper RRB/C-18, NPL, Feb. 14, 
1941. CP-510-M1 

258. Echo Intensities and Attenuation Due to Clouds, Rain, 

Hail, Sand and Duststorms at Centimeter Wavelengths, 

J. W. Ryde, OSRD WA-81-25, Report 7831, GEC, 

Oct. 13, 1941. CP-511-Ml 

259. The Atmospheric Absorption of Microwaves (in Third 
Conference Report of CP), J. H. Van Vleck, Report 
175 (43-2), RL, Apr. 27, 1942. (See reference 10.) 

Div. 14-121.1-M4 

260. The Effect of Rain Upon the Propagation of 1-Cm Elec¬ 
tro-Magnetic Waves, Case 22098, S. D. Robertson, Re¬ 
port MM-42-160-87, BTL, Aug. 1, 1942. CP-511-M2 

261. The Effect of Rain on the Propagation of Microwaves, 

Case 22098, A. P. King and S. D. Robertson, Report 
MM-42-160-93, BTL, Aug. 26, 1942. CP-511-M3 






270 


BIBLIOGRAPHY—VOLUME 1 


262. Comparison of Theoretical and Experimental Values for 
the Attenuation of 1-Centimeter Waves in Rain, Case 22098, 
S. D. Robertson, Report MM-43-160-2, BTL, Jan. 5, 

1943. CP-511-M4 

263. An Investigation on the Number and Size Distribution of 
Water Particles in Nature, Josef Mazur, F/Lt. Polish Air 
Force, OSRD II-5-6306(S), Report MRP-109, Meteoro¬ 
logical Research Committee, Great Britain, June 1943. 

CP-511-M5 

264. Report on the Absorption and Refraction of Electro-Mag¬ 

netic Waves by the Liquid Water, Water Vapour and Fog or 
Rain, N. F. Mott, OSRD II-5-4936, Reference 43/2881, 
CRB, Sept. 2, 1943. CP-510-M2 

265. Report on the Absorption of Electromagnetic Waves in the 

Wavelength Range 1-100 Cm by Water in the Atmosphere, 
N. F. Mott, OSRD II-5-4937, Reference 43/2882, CRB, 
Sept. 2, 1943. CP-510-M3 

266. Verification of Mie Theory, Calculations and Measure¬ 

ments of Light Scattering by Dielectric Spherical Particles 
(Progress Report), Victor Iv. LaMer, OSRD 1857, 
OEMsr-148, Service Project CWS-1, Division 10, NDRC, 
Columbia University, Sept. 29, 1943. CP-512-M1 

267. The Absorption of Centimetric Radiation by Atmospheric 
Gases, J. M. Hough, ADRDE, USWP-WC, Apr. 27, 

1944. CP-510-M4 

268. Attenuation Due to Water Drops in the Atmosphere, J. M. 
Hough, ADRDE, USWP-WC, Apr. 28, 1944. 

CP-511-M6 

269. Propagation of K/2 Band Waves, G. E. Mueller, Report 

MM-44-160-150, BTL, July 3, 1944. CP-511-M7 

270. Preliminary Note on Secure Communications on Milli¬ 

metre Waves, OSRD WA-2868-3, JEIA 5597, Report 
L/M40/WBL, TRE, Sept. 11, 1944. CP-510-M5 

271. Rotational Line Width in the Absorption Spectrum of At¬ 
mospheric Water Vapor and Supplement, Arthur Adel, 
OEMsr-1361, NDRC Division 14 Report 320, University 
of Michigan, Oct. 10, 1944; Supplement Feb. 1, 1945. 

CP-510-M6 

272. The Absorption of One-Half Centimeter Electromagnetic 
Waves in Oxygen, E. R. Beringer, OEMsr-262, Service 
Project AN-25, Division 14 Report 684, RL, Jan. 26, 

1945. CP-510-M7 

273. The Effect of Rain on Radar Performance, S. C. Hight, 
Report MM-44-170-50, BTL, Oct. 17, 1944. CP-511-M8 

274. Measurements of Wave Propagation, G. E. Mueller, Report 

MM-45-160-17, BTL, Feb. 5, 1945. CP-511-M9 

275. Further' Theoretical Investigations on the Atmospheric Ab¬ 

sorption of Microwaves, John H. Van Vleck, OEMsr-262, 
Service Project AN-25, Division 14 Report 664, RL, 

Mar. 1, 1945. CP-510-M8 

276. Measurements of the Attenuation of K-Band Waves by 
Rain, G. T. Rado, OEMsr-262, Service Project AN-25, 
Division 14 Report 603, RL, Mar. 7, 1945. 

CP-511-M10 

277. Attenuation of Centimetre and Millimetre Waves by Rain, 
Hail, Fogs, and Clouds (Draft), J. W. Ryde and D. Ryde, 
OSRD WA-5181-10, Report 8670, GEC, May 18, 1945. 

CP-511-M11 


278. The Relation Between Absorption and the Frequency De¬ 

pendence of Refraction (Fourth Conference), John H. Van 
Vleck, OEMsr-262, Division 14 Report 735, RL, May 28, 
1945. (See reference 12.) Div. 14-122.24-M4 

279. Absorption and Scattering of Microwaves by the Atmos¬ 
phere (Fourth Conference), Louis Goldstein, Report 
WPG-11, CUDWR, May 1945. (See reference 12.) 

280. C.V.D. Progress Report for May, 1945. The Absorption of 
K-Band Radiation in Gaseous Ammonia (Part I), Progress 
Report, CVD-CL, May 1945. 

281. K-Band Attenuation Due to Rainfall, Lloyd J. Anderson, 
J. P. Day, C. H. Freres, John B. Smyth, A. P. D. Stokes 
and L. G. Trolese, Report WP-20, NRSL, June 8, 1945. 

CP-511-M12 

282. A New Method for Measuring Dielectric Constant and Loss 

in the Range of Centimeter Waves, S. Roberts and Arthur 
R. von Hippel; Wave Guides with Dielectric Sections, L. J. 
Chu, Report 102, MIT, March 1941. CP-521-M1 

283. The Electrical Properties of Ice, T. A. Taylor and Willis 

Jackson, OSRD W-126-42, Report AC-1516, RDF 110, 
Com. 78, RDF, Dec. 22,1941. CP-522.13-M1 

284. The Dielectric Constant and Loss Factor of Water Vapor 

at a Wavelength of 9 Cm, Frequency 3380 Me/s, J. A. Sax¬ 
ton, OSRD W-203-2, Paper RRB/S-1, NPL-DSIR 
Mar. 31, 1942. CP-522.12-M1 

285. The Dielectric Constant of Water Vapour and its Effect upon 
the Propagation of Very Short Waves, A. C. Stickland, 
OSRD WA-175-7, Paper RRB/S-2, NPL-DSIR, May 11, 

1942. CP-522.12-M2 

286. Progress Report on Ultrahigh Frequency Dielectrics, Arthur 
R. von Hippel, OEMsr-191, Division 14 Report 121, 
MIT, Laboratory for Insulation Research, January 1943. 

CP-521-M2 

287. Conductivities of Sea, Tap and Distilled Water at X = 10 

Cm., L. B. Turner, OSRD WA-649-1, Report M-496, 
ASE, April 1943. CP-522.11-,Ml 

288. The Measurement of Dielectric Constant and Loss with 

Standing Waves in Coaxial Wave Guides, Arthur R. von 
Hippel, D. G. Jelatis, and W. B. Westphal, OEMsr- 
191, Division 14, Report 142, MIT, Laboratory for Insu¬ 
lation Research, April 1943. CP-521-M4 

289. The Dielectric Constant and Absorption Coefficient of 
Water Vapour for Wavelengths of 9 Cm and 3.2 Cm, 
Frequencies 8,330 and 9,350 Mc/s., J. A. Saxton, Paper 
RRB/S-11, NPL-DSIR, June 14, 1943. CP-522.12-M3 

290. “Electrical Measurements on Soil with Alternating Cur¬ 
rents,” R. L. Smith-Rose, Journal of the Institution of 
Electrical Engineers (London), NPL, Voi. 75, August 

1943, pp. 221-237. CP-522.3-M1 

291. Memorandum on an Electrical Method of Measuring the 
Dielectric Constant of Atmospheric Air, and Recording 
it Continuously, OSRD WA-1464-7, Report JMRP-8, 
Report M/Memo-15/PEC, TRE, Jan. 6, 1944. 

CP-522.2-MI 

292. The Dielectric Constant and Absorption Coefficient of 
Water Vapour for Radiation of Wavelength 1.6 Cm, 
Frequency 18,800 Mc/s., J. A. Saxton, Paper RRB/S.17, 
NPL-DSIR, Apr. 22, 1944. 

293. The Dielectric Constant of Water and Ice at Centimetre 

Wavelengths (Working Committee), J. M. Hough, 
ADRDE, USWP-WC, Apr. 28, 1944. CP-522.1-M1 




271 


BIBLIOGRAPHY—VOLUME 1 


294. Preliminary Report on the Dielectric Properties of Water 
in the K-Band, C. H. Collie, Report CL Misc. 25, CVD, 
May 1944. 

295. Recent Dielectric Constant and Loss Tangent Measure¬ 

ments on X-Band (Radome Bulletin No. 5), Elizabeth 
M. Everhart, OEMsr-262, Division 14 Report 483-5, 
RL, July 14, 1944. CP-522.4-M1 

Div. 14-234.5-M5 

296. Dielectric Properties of Water and Ice at K-Band, E. L. 

Younker, OEMsr-262, Service Project AN-25, Division 
14 Report 644, RL, Dec. 4, 1944. CP-522.1-M2 

297. The Interaction Between Electromagnetic Fields and Di¬ 

electric Materials, Arthur R. von Hippel and R. G. 
Breckenridge, OEMsr-191 Division 14 Report 122, 
MIT, Laboratory for Insulation Research, January, 
1943. CP-521-M3 

298. The Dielectric Properties of Water at Wavelengths from 

2 Cm to 10 Cm and over the Temperature Range 0° to 40° 
C, J. A. Saxton, OSRD WA-4340-5, Paper RRB/C-115, 
NPL-DSIR, Mar. 20, 1945. CP-522.11-M2 

299. The Dielectric Properties of Water in the Temperature 
Range 0° C to 40° C for Wavelengths of 1.24 Cm and 

I. 58 Cm, J. A. Saxton and J. A. Lane, JEIA 9811, Paper 
RRB/C.116, NPL-DSIR, Mar. 7, 1945. 

300. The Anomalous Dispersion of Water at Very High Radio 

Frequencies in the Temperature Range 0° to 40° C, J. A. 
Saxton, OSRD WA-4459-8, JEIA 9812, Paper RRB/C- 

118, NPL-DSIR, Apr. 6, 1945. CP-522.11-M3 

301. Centimeter Wave Propagation over Sea Within the Op¬ 

tical Range, H. Archer-Thomson, J. C. Dix, F. Hoyle, 
E. C. S. Megaw, and M. H. L. Pryce, OSRD W-157-16, 
Report M-398, ASE, January 1942. CP-532.2-M1 

302. Preliminary Report on the Reflection of 9-Cm Radiation 

at the Surface of the Sea, H. Archer-Thomson, N. Brooke, 
T. Gold, and F. Hoyle, OSRD WA-1131-2, Report M-542, 
ASE, September 1943. CP-532.2-M2 

303. Comment on the Reflection of Microwaves from the Sur¬ 

face of the Ocean (Part II), S. O. Rice, Report MM-43- 
210-6, BTL, Oct. 13, 1943. CP-532.2-M3 

304. S-Band Measurements of Reflection Coefficients for Var¬ 
ious Types of Earth, E. M. Sherwood, Report 5220.129, 
Sperry Gyroscope Company, Oct. 29, 1943. CP-532.1-MI 

305. Special Report on the Determination of the Coefficient of 

Reflection of Radio Waves at the Ground by Means of 
Radar Observations, W. Sterling Ament, Report RA- 
3A-212A, NRL, Nov. 10, 1943. CP-532.1-M2 

306. Scattering, T. L. Eckersley, OSRD WA-2255-1F, JEIA 
3904, Report TR-481, BRL, November 1943. 

CP-512-M3 

307. Preliminary Measurements of 10 Cm Reflection Co¬ 
efficients of Land and Sea at Small Grazing Angles, Pearl 

J. Rubenstein and William T. Fishback, Division 14 

Report 478, RL, Dec. 11, 1943. CP-532-M1 

308. Further Measurements of 3- and 10-Cm Reflection Co¬ 
efficients of Sea Water at Small Grazing Angles, William 
T. Fishback and Pearl J. Rubenstein, OEMsr-262, Di¬ 
vision 14 Report 568, RL, May 17, 1944. CP-532.2-M4 

309. Microwave Propagation Studies, The Reflection of Sound 
Signals in the Atmosphere, Case 37003, File 36691-1, 


F. H. Willis, Report MM-44-160-156, BTL, July 3 
1944. 

310. Interim Report on Experiments on Ground Reflection at 
a Wavelength of 9 Cm, L. H. Ford, JEIA 4899, Paper 
RRB/C.101, DSIR, July 7, 1944. 

311. An Experimental Investigation of the Reflection and Ab¬ 

sorption of Radiation of 9-Cm Wavelength, L. H. Ford 
and R. Oliver, OSRD WA-3386-2, Paper RRB/C-107, 
DSIR, Oct. 27, 1944. CP-532-M2 

312. The Measurement of High Reflections at Low Power 

(Radome Bulletin No. 7), Raymond M. Redheffer, 
OEMsr-262, Division 14 Report RL-483-7, RL, Nov. 
20, 1944. CP-531-M3 

313. Ground Reflection Coefficient Experiments on X-Band, 

Case 20564, W. M. Sharpless, Report MM-44-160-250, 
BTL, Dec. 15, 1944. CP-532.1-M3 

314. The Reflection Coefficient of a Linearly Graded Layer, 

OSRD WA-3438-5, Report TR-492, BRL, December 
1942. CP-531-M2 

315. Reflection and Scattering, T. L. Eckersley, OSRD WA- 
4002-12, Report TR-506, BRL, January 1945. 

CP-532.2-M5 

316. Reflection from an Inversion, L. E. Beglian and F. J. 
Northover, OSRD WA-4494-14, JEIA 9997, Report 
AC-8210, USW-140, USW, May 24, 1945. CP-531-M5 

317. Notes on the Comparison of Vertical and Horizontal Po¬ 

larization in Ground Wave Propagation, G. Millington, 
OSRD WA-1463-5, Report TR/442, BRL, January 
1940. CP-540-M1 

318. Horizontal and Vertical Polarization, T. L. Eckersley, 
OSRD II-5-5280, Report TR-441, BRL, July 1942. 

CP-540-M2 

319. The Investigation of Horizontally and Vertically Polar¬ 
ized Direction Finding on Frequencies of the Order of 
20 to 70 Megacycles per Second, T. L. Eckersley, OSRD 
II-5-5284, Report TR-451, BRL, September 1942. 

CP-540-M3 

320. Polarization Effects and Aerial System Geometry at Cen¬ 
timeter Wavelengths, E. C. S. Megaw, H. Archer-Thom¬ 
son, and E. M. Hickin, Report 8101, GEC, Nov. 26, 
1942. 

321. Change of Polarization as a Means of Gap Filling, Richard 
A. Hutner, Francis Parker, Bernard Howard, and Joc¬ 
elyn Gill, Division 14 Report C-7, RL, Dec. 28, 1942. 

CP-540-M4 

322. Vertical Polarization vs Horizontal Polarization, Ralph 

C. Loring, Tentative Technical Report T-l, CESL, 
Oct. 22, 1943. CP-540-M5 

323. The Depolarization of Microwaves, M. Kessler, C. E. 

Mandeville and E. L. Hudspeth, Division 14 Report 
458, RL, Nov. 1, 1943. CP-540-M6 

324. Polarization Studies at S and X Frequencies, O. J. Baltzer, 
W. M. Fairbank, and J. D. Fairbank, OEMsr-262, 
Division 14 Report 536, RL, Mar. 14, 1944. CP-540-M7 

325. Screening by Hills, H. G. Booker, OSRD WA-1105-3C, 

Report T-1015, TRE, May 1941. CP-231.222-MI 

326. Diffraction Round a Sphere or Cylinder, G. Millington, 
OSRD II-5-5703, Report TR-433, BRL, March 1942. 

CP-231.21-MI 



272 


BIBLIOGRAPHY—VOLUME 1 


327. Centimeter Wave Transmission Measurements from an Ur¬ 
ban Site, H. Archer-Thomson, E. M. Hickin, and E. C. S. 
Megaw, Report 8034, GEC, July 28, 1942. 

328. Report on an Investigation of the Propagation of Centimeter 

Waves over Ridges and Through Trees, R. L. Smith-Rose, 
OSRD WA-772-19, Report AC-4345, Com. 181, NPL, 
June 2, 1943. CP-231.22-M1 

329. A Note on the Propagation of K-Band Waves Through 

Trees, Case 22098, S. D. Robertson, Report MM-43-160- 
129, BTL, Aug. 13, 1943. CP-231.221-M1 

330. Report on Further Experiments on the Propagation of 

Centimeter Waves Through Trees in Leaf and over Level 
Ground, OSRD WA-1337-3, Report AC-5059, Com. 197, 
NPL, Sept. 6, 1943. CP-231.221-M2 

331. Centimeter Wave Propagation, Notes on the Effect of Ob¬ 
struction by a Single Tree, R. E. Jennings, E. C. S. Megaw, 
H. Archer-Thomson, and E. M. Hickin, OSRD WA- 
1356-6, Report M-565, ASE, October 1943. 

CP-231.221-M3 

332. An Experimental Investigation on the Propagation of 
Radio Waves over Bare Ridges in the Wavelength Range 10 
Centimetres to 10 Metres, Frequencies 30 to 3000 Mc/s, 
J. S. McPetrie and L. H. Ford, OSRD WA-1463-17, 
Paper RRB/S-12, NPL-DSIR, Oct. 1, 1943. 

CP-231.222-M2 

333. Some Observed Effects of Trees upon Microwave Propaga¬ 
tion, Case 37003, File 36691-1, A. C. Peterson, Report 
MM-43-160-150, Sept. 17, 1943, Revised Oct. 15, 1943. 

CP-231.221-M4 

334. Effect of Hills and Trees as Obstructions to Radio Propaga¬ 

tion, Delmer C. Ports, OSRD 3070, OEMsr-1010, Jansky 
and Bailey, November 1943. CP-231.22-M2 

335. Report on Some Further Experiments on the Effect of Ob¬ 
stacles on the Propagation of Centimetre Waves, L. H. Ford, 
A. C. Grace, and J. A. Lane, JEIA 3157, Report AC-5876, 
NPL-RD, USW, Jan. 20, 1944. 

Addendum, R. L. Smith-Rose, OSRD WA-3822-12, Re¬ 
port AC-5876a, NPL, Jan. 1, 1945. CP-231.223-MI 

336. The Propagation of Ultra Short Waves Round Hills and 
Other Obstacles, T. L. Eckersley, OSRD WA-2884-3, 
JEIA 5674, Report TR-479, BRL, May 1944. 

CP-231.222-M3 

337. Scattering of Radio Waves by Metal Wires and Sheets, F. 
Horner, JEIA 7793, Paper RRB/C-110, DSIR, Jan. 1, 
1945. 

338. Some Experiments on the Propagation over Land of Radi¬ 
ation of 9.2-Cm Wavelength, L. H. Ford, OSRD WA- 
4297-8, Paper RRB/C-113, NPL-DSIR, Feb. 15, 1945. 

CP-231.22-M3 

339. A Preliminary Study of Ground Reflection and Diffraction 

Effects with Centimetric Radar Equipment, J. S. Hey, F. 
Jackson, and S. J. Parsons, OSRD WA-5062-2, Report 
274, AORG, June 28, 1945. CP-231.21-M2 

340. Diffraction at Coast Line, Sloping Site, H. G. Booker, 
OSRD WA-986-6c, Report 10, TRE, May 1, 1941. 

CP-233-M2 

341. Mixed Land and Sea Transmissions, T. L. Eckersley, 
OSRD II-5-5515, Report E-16, BRL, October 1941. 

CP-233-M3 


342. Diffraction at Coast Line, Further Numerical Examples, 

H. G. Booker, OSRD WA-92-5d, Report M-35, TRE, 
Feb. 5, 1942. CP-233-M4 

343. Coastal Refraction, OSRD II-5-5281, Report TR-436, 

BRL, May 1942. CP-233-M5 

344. Propagation of Wireless Waves over Ground of Varying 

Earth Constants (Part Land and Part Sea), G. Millington, 
OSRD II-5-5277, Report TR-440, BRL-Marconi, Ltd., 
July 1942. CP-233-M6 

345. Transmission over Ground of Varying Earth Constants, 
OSRD 11-5-5457, Report TR-473, BRL, July 1943. 

CP-233-M8 

346. Diffraction at Coast Line (Appendix to Report on Siting 

of RDF Stations), H. G. Booker, OSRD WA-986-6b, 
Report 6, TRE, Jan. 27, 1944. CP-233-M1 

347. Siting and Coverage of Ground Radars, E. J. Emmerling 

OEMsr-1207, Report WPG-10, CUDWR, May 1945. 
(See reference 12.) CP-202.4-M6 

348. Scattering and Spurious Echoes, T. L. Eckersley, OSRD 
II-5-5275, Report TR-437, BRL, April 1942. 

CP-621.7-MI 

349. Reflection of 10-Cm Radiation by Model Aircraft, A. F. 
Phillips, Christchurch Report 174, ADRDE, Sept. 8, 

1942. 

350. Elementary Survey of Scattering and Echoing by Elevated 
Targets, H. G. Booker, Report M/48/HGB, TRE, 
December 1942. 

351. The Resolution of Composite Echoes with Centimeter Wave 
R.D.F., J. R. Benson, J. A. Ramsay, and P. B. Blow, 
OSRD WA-1789-2, Report 4070/C/104, CAfeE, Feb. 10, 

1943. CP-623-M3 

352. Microwave Radar Reflection, J. F. Carlson and S. A. 
Goudsmit, Division 14 Report 43-23, RL, Feb. 20, 1943. 

CP-623-M4 

353. Reflection of Radar Waves from Targets of Simple Geomet¬ 

ric Form, Lloyd J. Anderson, John B. Smyth, and F. R. 
Abbott, BuShips Problem X4-49CD, Report WP-3, 
NRSL, Feb. 24, 1943. CP-612.4-M1 

354. Radar Echoes from Periscopes, John E. Freehafer, Divi¬ 
sion 14 Report 42-1, RL, Mar. 1, 1943. CP-622.1-MI 

355. Radar Echoes from Atmospheric Phenomena, Arthur E. 
Bent, Division 14 Report 42-2, RL, Mar. 13, 1943. 

CP-621.1-MI 

356. Echoes Produced by Perfectly Conducting Objects of Certain 
Simple Shapes in Free Space, R. E. B. Makinson OSRD 
II-5-5691, Report RP-173, CSIR, Mar. 25, 1943. 

CP-622.5-M1 

357. Gratings and Screens as Microwave Reflectors, Division 14 

Report 54-20, RL, Apr. 1, 1943. CP-611-M1 

358. Report on an Investigation into the Nature of Sea Echoes, 
OSRD WA-1142-3, Report T-1497, TRE, May 12, 1943. 

CP-621.6-MI 

359. The Application of Corner Reflectors to Radar ( Theoreti¬ 
cal), R. D. O’Neil, F. S. Holt, and Prescott D. Crout, 
Division 14 Report 43-31, RL, May 14, 1943. 

CP-611.1-MI 

360. The Application of Corner Reflectors to Radar (.Experi¬ 

mental ), R. D. O’Neil, Division 14 Report 55-4, RL> 
July 1, 1943. CP-611.1-M2 




BIBLIOGRAPHY—VOLUME 1 


273 


361. Measurement of the Effective Echoing Areas of Various 

Aircraft, Ross Bateman, Report ORG-P-8-1, OCSO, July 
2, 1943. CP-622.3-M1 

362. Overwater Observations at X and S Frequencies on Surface 

Targets, O. J. Baltzer, V. A. Counter, W. M. Fairbank, 
W. O. Gordy, and E. L. Hudspeth, Division 14 Report 
401, RL, July 26, 1943. CP-612.3-M1 

363. Towed Radar Targets, G. A. Armstrong and G. H. Beech¬ 

ing, OSRD WA-1012-2, Research Report 212, ADRDE, 
Aug. 6, 1943. CP-612.2-M1 

364. Corner Reflector Tests at Langley Field, C. M. Gilbert, 
Division 14 Report 402, RL, Aug. 6, 1943. 

CP-611.1-M3 

365. Properties of Corner Reflectors, Case 22098, S. D. Robert¬ 
son, Report MM-43-160-130, BTL, Aug. 12, 1943. 

CP-611.1-M4 

366. Use of Corner Reflectors as IFF on Ships, OSRD II-5- 

5680, Operational Research Report 24, Australian ORS 
and CSIR-RL, Aug. 30, 1943. CP-611.1-M5 

367. An Investigation into the Nature of Sea Echoes, A. C. 
Cossor, Ltd., JEIA 1221, Report MR-109, Research De¬ 
partment Myra Works, London E10, Sept. 8, 1943. 

368. The Scattering of Radiation from Rectangular Planes, 
Half-Cylinders, Hemispheres, and Airplanes, Contract 
W-2279sc-551, Item 3, Moore School of Engineering, 
University of Pennsylvania, Oct. 12, 1943. CP-512-M2 

369. On the Appearance of the A-Scope when the Pulse Travels 
Through a Homogeneous Distribidion of Scatterers, A. J. F. 
Siegert, Division 14, Report 466, RL, Nov. 9, 1943. 

Div. 14-124.2-M2 

370. On the Fluctuations in Signals Returned by Many Inde¬ 
pendently Moving Scatterers, A. J. F. Siegert, Division 14 
Report 465, RL, Nov. 12, 1943. Div. 14-122.113-M7 

371. The Use of Permanent Echo Amplitudes for Monitoring 

S-Band Radar Equipment, F. J. Kerr and J. F. McCon¬ 
nell, OSRD II-5-5750, Report RP-177/2, CSIR-RL, 
Dec. 7, 1943. CP-623-M5 

372. The Range Calculator, S. J. Mason, Division 14 Report 

497, RL, Dec. 20, 1943. CP-202.4-M2 

373. The Performance of 10-Cm Radar on Surface Craft, B. F. 

Schonland, OSRD WA-1570-39, Report 155, AORG, 
Jan. 3, 1944. CP-202.312-M1 

374. Special Report on Radar Cross Section of Ship Targets, 

Martin Katzin, Report RA-3A-213A, NRL, Jan. 24, 
1944. CP-612.1-MI 

375. Observations of Life Rafts Equipped with Corner Re¬ 

flectors, Emmett L. Hudspeth and John P. Nash, Divi¬ 
sion 14 Report 533, RL, Feb. 15, 1944. CP-611.1-M6 

376. Radar Cross Section of Ship Targets (Part II), W. Sterling 

Ament, Martin Katzin, and F. C. MacDonald, Report 
R-2232, NRL, Feb. 18, 1944. CP-612.1-MI 

377. Optical Theory of the Corner Reflector, R. C. Spencer, 
OEMsr-262, Division 14 Report 433, RL, Mar. 2, 1944. 

CP-611.1-M7 

378. Observations on Signal Stability at S and X Frequencies, 

Otto J. Baltzer, Jr., William M. Fairbank, and J. D. 
Fairbank, OEMsr-262, Division 14 Report 537, RL, 
Mar. 14, 1944. CP-632-M1 

379. Interim Report on the Recognition of Radar Echoes, F. E. 
S. Alexander, OSRD II-5-5796(S), JEIA 3401, Report 
RD-1/353, RDL-DSIR, NZ, Mar. 20, 1944. CP-623-M6 


380. Screened and Unscreened Radar Coverage for Surface 
Targets, W. Walkihshaw and J. E. Curran, OSRD WA- 
2284-2, Report T-1666, TRE, March 1944. 

CP-612.3-M2 

381. The Performance of Naval Radar Systems Against Air¬ 

craft, F. Hoyle, OSRD WA-2255-lo, Report JEIA-3902, 
ASE, Apr. 3, 1944. CP-202.11-M2 

382. Preliminary Report on the Fluctuations of Radar Signals, 

H. Goldstein and Paul D. Bales, OEMsr-262, Division 
14 Report 569, RL, May 16, 1944. CP-632-M2 

383. Radar Ranging on Land Targets, OSRD II-5-6178(S), 
Memorandum 101/G-36/ALH, TRE, May 18, 1944. 

CP-202.4-M3 

384. The Radar Echoing Power of Conducting Spheres, T. 

Pearcey, and J. M. C. Scott, OSRD WA-2334-6, Report 
CR-228, ADRDE, May 24, 1944. CP-623-M7 

385. Use of Corner Reflectors in Beaconry, F. J. Kerr, OSRD 

II-5-6145(S), JEIA 5180, Report RP-200, CSIR-RL, 
June 8, 1944. CP-611.1-M8 

386. Calibration and Standardization of Land Based Radars by 

the Use of Small Plane Targets, F. R. Abbott, BuShips 
Problem X4-49CD, Report WP-12, NRSL, June 10, 
1944. CP-612.5-M1 

387. Test of the Pre-Production Model Corner Reflector, Final 

Report of Project E-44-S7, Alvin E. Hebert and C. B. 
Overacker, AAF Board Project (M-3) 69-Eglin Field, 
Fla., Report 413.44/R387.1, Intel. Br. OCSO-USA, 
June 17, 1944. CP-611.1-M9 

388. Radar Cross Section of Ship Targets (Part III), W. Sterl¬ 

ing Ament, Martin Katzin, and F. C. MacDonald, Re¬ 
port R-2295, NRL, June 27, 1944. CP-612.1-M1 

389. Notes on Echoes and Atmospherics from Lightning Flashes 
on P Band, J. L. Pawsey, OSRD II-5-6144(S), JEIA 
5177, Report RP-49-2, CSIR-RL, July 11, 1944. 

CP-621.3-MI 

390. Theory of Ship Echoes as Applied to Naval RCM Opera¬ 

tions, T. S. Kuhn and Peter J. Sutro, OEMsr-411, Re¬ 
search Project RP-186, Report 411-93, Harvard Uni¬ 
versity, RRL, July 14, 1944. Div. 15-221.11-M2 

391. Radar Echoes from the Nearby Atmosphere, Case 37003-4, 

Millard W. Baldwin, Jr., Report MM-44-150-2, BTL, 
July 18, 1944. CP-621-M1 

392. Radar Cross Section of Ship Targets (Part IV), W. Sterl¬ 

ing Ament, Martin Katzin, and F. C. MacDonald, Re¬ 
port R-2332, NRL, July 21, 1944. CP-612.1-M1 

393. Radar Echoes from the Nearby Atmosphere, Second Report, 

Case 37003-4, Millard W. Baldwin, Jr., Report MM-44- 
150-3, BTL, July 31, 1944. CP-621-M1 

394. Reflecting Properties of Metal Gratings, J. S. Gooden, 

OSRD II-5-6230(S), Report RP-215, CSIR-RL, July 
31, 1944. CP-611-M2 

395. Theory of the Performance of Radar on Ship Targets 

(ADRDE and CAEE Joint Report), M. V. Wilkes, J. A. 
Ramsay, and P. B. Blow, OSRD WA-2843-10, ADRDE 
Reference R04/2/CR252, CAEE Reference 69/C/149, 
July 1944. CP-612.1-M2 

396. Corner Reflectors for Life Rafts, Emmett L. Hudspeth and 

John P. Nash, OEMsr-262, Division 14 Report 608, RL, 
Aug. 1, 1944. CP-611.1-M 10 



274 


BIBLIOGRAPHY—VOLUME 1 


397. The Characteristics of S-Band Aircraft Echoes with Par¬ 
ticular Reference to Radar A.A. No. 3 MK. II. G. H. 
Beeching and N. Corcoran, OSRD WA-2812-13, Re¬ 
search Report 253, ADRDE, Aug. 4, 1944. 

CP-622.3-M2 

398. Radar Echoes from the Nearby Atmosphere, Third Report, 

Case 37003-4, Millard W. Baldwin, Jr., Report MM-44- 
150-4, BTL, Aug. 11, 1944. CP-621-M1 

399. Considerations Concerning Radar Coverage Diagrams, 

J. L. Pawsey, OSRD II-5-6229(S), Report RP-217, 
CSIR-RL, Aug. 14, 1944. CP-202.4-M5 

400. RDF Echoes to be Expected from Objects of Various Shapes, 

OSRD WA-6-21, Extra Mural Res. F.72/80, Report 26, 
Ministry of Supply, DSR. CP-622.5-M2 

401. Radar Echoes from Shells Bursts at 4 Meters and 50-Cm 

Wavelengths, S. M. Taylor and F. E. W. Bugler, Research 
Report 260, RRDE, Oct. 9, 1944. CP-622.4-M1 

402. Summer Storm Echoes on Radar MEW, J. S. Marshall, 

R. C. Langille, William M. Palmer, R. A. Rodgers, G. P. 
Adamson, and F. F. Knowles, Report 18, CAORG, Nov. 
27, 1944. CP-621.1-M2 

403. The Cancellation of Permanent Echoes by the Use of Co¬ 

herent Pulses (Interim Report), H. Grayson, OSRD WA- 
3482-7C, Technical Note RAD-253, RAE, November 
1944. CP-623-M8 

404. The Fading of S-Band Echoes from Ships in the Optical 

Zone, R. I. B. Cooper, OSRD WA-3677-8, Research 
Report 265, Dec. 12, 1944. CP-622.2-M3 

405. Rotating Corner-Reflectors for Ship Identification, Julian 

M. Sturtevant, OEMsr-262, Division 14 Report 654, 
RL, Jan. 1, 1945. CP-611.1-M11 

406. Reflection from Smooth Curved Surfaces, R. C. Spencer, 
OEMsr-262, Division 14, Report 661, RL, Jan. 26, 1945. 

CP-531-M4 

407. Analysis of Over-Water Tracking, Elizabeth J. Campbell, 

OEMsr-262, Service Project NO-166, Division 14 Report 
695, RL, Feb. 12, 1945. CP-202.12-MI 

408. Technical Report on the Maximum Range of Detection of 
the German Early Warning Radar Equipment, Especially 
when Viewing Large, Tight Formations of Bomber Air¬ 
craft, W. E. Bales and K. A. Norton, Report OAD-13, 
ORS, VIII Bomber Command OCSO, Sept. 13, 1943. 

CP-202.4-MI 

409. Performance Checks and Estimation of Vessel Size on 
Short-Based 10-Cm Radar Sets, D. Lack, OSRD WA- 
1992-3, JEIA 3124, AORG, Mar. 30, 1944. 

CP-622.2-MI 

410. Report of Trials to Determine the Variations of the Appar¬ 

ent Reflecting Point of Plain 10-Cm Waves from a Destroyer, 
J. F. Coales and M. Hopkins, OSRD WA-3702-1, Report 
M-627, ASE, July 1944. CP-622.2-M2 

411. The Reflection of Electromagnetic Waves by Long Wires and 
Non-Resonant Cylindrical Conductors, J. M. C. Scott and 
T. Pearcey, JEIA 7286, Research Report 259, RRDE, 
Nov. 13, 1944. 

412. Theory of Radar Return from the Schnorkel, P. M. Marcus, 
OEMsr-262, Division 14 Report 671, RL, Jan. 15, 1945. 

CP-622.1-M2 

413. Sea Returns and the Detection of Schnorkel, G. G. Mac- 
farlane, OSRD WA-4196-8, JEIA 8643, Report T-1787, 
TRE, Feb. 13, 1945. (See reference 418.) CP-622.1-M3 


414. Interservice KXS-Band Radar Trials; Over Water Per¬ 

formance Against Surface Targets, J. A. Ramsay, P. B. 
Blow, and H. J. Worsdall, JEIA 8820, Report M-688, 
ASE, February 1945. CP-612.3-M3 

415. An Observation of Diffuse Cloud-Like Echoes, J. L. Paw¬ 

sey and F. J. Kerr, OSRD II-5-7007(S), Report RP-246, 
CSIR-RL, Mar. 6, 1945. CP-621.4-M1 

416. The So-Called Standard Target, A. H. Brown, OEMsr- 
262, Division 14 Report S-43, RL, Mar. 10, 1945. 

CP-612.6-MI 

417. Radar Cross Section of Ship Targets (Part V), F. C. Mac¬ 
Donald, Report R-2466, NRL, Mar. 12, 1945. 

CP-612.1-MI 

418. Radar Results Against Schnorkels: A Commentary on TRE 

T-l 787, Sea Returns and the Detection of Schnorkel, OSRD 
WA-4276-5, JEIA 9111, Report 338, ORS/CC, Mar. 16, 
1945. (See reference 413.) CP-622.1-M4 

419. Radar Echoes from Clouds of Water Droplets, F. Hoyle, 
Report AC-7930, Report 128, USW, Mar. 16, 1945. 

420. Comments on Radar Echoes from Water Droplets, (Paper 

AC-7930, USW Report 128), R. G. Ross, OSRD WA- 
4149-10, Paper AC-7931, Report 129, USW, Mar. 16, 
1945. CP-621.2-MI 

421. Radar Cross Section of Ship Targets (Part VI) W. J. Barr, 

Report R-2467, NRL, Apr. 10, 1945. CP-612.1-M1 

422. S-Band Radar Echoes from Snow, R. C. Langille, J. S. 

Marshall, William M. Palmer, and L. G. Tibbies, Report 
26, CAORG, June 14, 1945. CP-621.5-Ml 

423. Surface Coverage of Some Shipborne Radar Sets on S, X, 

and K Bands, J. D. Fairbank and W. M. Fairbank, 
OEMsr-262, Service Projects NS-234 and NS-175, Divi¬ 
sion 14 Report 720, RL, June 15, 1945. CP-202.4-M7 

424. Echoes from Tropical Rain on X-Band Airborne Radar, 

Arthur E. Bent, OEMsr-262, Division 14 Report 728, 
RL, June 15, 1945. CP-621.2-M2 

425. Analysis of Storm Echoes in Height Using MHF, J. S. 

Marshall, L. G. Eon, and L. G. Tibbies, Report 30, 
CAORG, June 25, 1945. CP-621.1-M3 

See also: Radar Camouflage, Division 14 Report 766, RL, 
July 16, 1945. CP-633-M1 

426. 3000-Megacycle Communication, H. H. Beverage, 

OEMsr-32, NDRC Projects SC-13 and PDRC-90, RCA, 
Mar. 10, 1942. CP-203.1-MI 

427. Microwave Telephone, Part I Omnidirectional, Part II, 

Directional, OEMsr-442, NDRC Projects C-42 and 
SC-13, RCA, Mar. 22, 1943. CP-203.1-M2 

428. Factors Determining the Range of Radio Communications 
in the Various Theaters of Operation, Jack W. Herbstreit, 
Report ORG-P-14-1, OCSO, June 3, 1943. CP-732-M1 

429. Radiotelephone Communication on 3000 Megacycles, Paul 

A. Anderson, K. E. Fitzsimmons, C. L. Barker, and S. T. 
Stephenson, OEMsr-728, NDRC Research Project 
PDRC-647, Division 14 Report 152, Report 2, Wash¬ 
ington State College, June 12, 1943. CP-203.1-M3 

430. An Analysis of the Effect of Frequency on Short Distance 
Radio Communications, Ross Bateman and William Q. 
Crichlow, Report ORB-P-15-1, OCSO, Aug. 18, 1943. 

CP-732.1-MI 

431. Use of the 25- to 50-Mc/s Band for Short Range Wireless 

Communication, OSRD WA-1022-3, Report 130, AORG, 
Aug. 27, 1943. CP-732.1-M2 



BIBLIOGRAPHY—VOLUME 1 


275 


432. Trials with a 250-Wait Frequency-Modulated VHF Sender 

Across a Sea Water Path Beyond the Optical Range, G. W. 
Higgins and W. H. Hill, OSRD WA-1352-5, Report 878, 
SRDE, September 1943. CP-712-M1 

433. Radio Communication in Jungles, Arthur C. Omberg, 

Report ORG-2-1, OCSO, Sept. 1, 1943. CP-711-MI 

434. Measurement of Factors Affecting Jungle Radio Com¬ 
munication, Jack W. Herbstreit and William Q. Crich- 
low, Report ORB-2-3, OCSO, Nov. 10, 1943. 

CP-711-M2 

435. Methods for Improving the Effectiveness of Jungle Radio 

Communication, Technical Bulletin Sig. 4, U.S. War 
Department, Jan. 14, 1944. CP-711-M3 

436. Survey of Existing Information and Data on Atmospheric 
Noise Level over the Frequency Range 1-30 Mc/s, H. A. 
Thomas and R. E. Burgess, OSRD WA-3201-2, JEIA 
2815, Paper RRB/C-90, DSIR, Feb. 21, 1944. 

CP-732-M2 

437. Methods of Reducing Radar Interference to Communication, 
Arthur C. Omberg, Joseph B. Epperson, and William Q. 
Crichlow, Report ORB-E-27-2, OCSO, Apr. 19, 1944. 

CP-731-M1 

438. The Application of Passive Repeaters to Point to Point 

Communication at VHF and UHF, Ross Bateman, Re¬ 
port ORB-P-20-1, OCSO, Apr. 29, 1944. CP-721-M1 

439sL.Summary of Radio Propagation Problems in Southwest 
Pacific Area, W. C. Babcock, JEIA 6298, Report US/ 
413.44/R113, Intel. Br. OCSO, Sept. 6, 1944. 

CP-713-M1 

439b .Point to Point Communication in MF and Via Ground 
Wave Propagation, W. C. Babcock, JEIA 6770, Report 
413.44/R423.4, Intel. Br. OCSO-SWPA, Aug. 15, 1944. 


440. Measurements of Factors Affecting Radio Communication 

& Lor an Navigation in SWPA, Ross Bateman, Jack W. 
Herbstreit, and Robert B. Zechiel, Report ORB-2-4, 
OCSO, Dec. 16, 1944. CP-713-M2 

441. Field Trials of Ultra Short Wave Frequency and Amplitude 
Modulated Multichannel Radio Telephone Systems, A. W. 
Pearson, W. J. Bray, J. H. H. Merriman, R. W. White, 
J. G. Hobbs, C. H. Gibbs, and H. Prain, Radio Report 
1115, POED, Mar. 27, 1944. 

442. Physics of the Air, W. J. Humphreys, McGraw-Hill Book 
Co., 1940, p. 457. 

443. Ergebnisse der Exakten Naturwissenshaften, H. Plendl 
and G. Eckart, Berlin, 17, 1938, p. 334. 

444. “Reflection of Waves in an Inhomogeneous Absorbing 
Medium,” P. S. Epstein, Proceedings of the National 
Academy of Sciences, 16, 1930, p. 627. 

445. “Penetration of a Potential Barrier by Electrons,” Carl 
Eckart, The Physical Review, 35, 1930, p. 1303. 

446. “The Relation of Drop Size to Intensity,” J. O. Laws 
and D. A. Parsons, Transactions of the American Geo¬ 
physical Union, 1943, p. 452. 

447. “Ultra Short Wave Propagation,” I. C. Schelleng, Chas. 
R. Burrows, and E. B. Ferrell, Bell System Technical 
Journal, y April 1933. (See reference 24.) 

448. Report JANP 102, Joint Communications Board. 

449. “On the Connection Formulas and the Solutions of the 
Wave Equation,” R. E. Langer, The Physical Review, 51, 
1937, p. 670. 

450. Treatise on Theory of Bessel Functions, George Neville 
Watson, Cambridge University Press, Second Edition, 
1944. 











I 


GENERAL BIBLIOGRAPHY OF REPORTS ON 
TROPOSPHERIC PROPAGATION 
REPORT WPG-14 


This Bibliography is a comprehensive tabulation of the body of scientific reports pertaining to wave propagation through 
the troposphere, compiled by the Columbia University Wave Propagation Group to about October 31, 1945. For convenience 
and clarity it has been divided into twenty sections, each dealing with a particular phase of propagation phenomena. The 
various headings are self-explanatory, and the list of sources and their abbreviated designations which precede the Bib¬ 
liography proper will be found helpful. 

In preparing the Bibliography, about 560 papers were considered. Of these, 115 were excluded as obsolete, or because their 
contents were included in other reports retained. An additional 46 papers dealing with doppler effect and the transmission 
of sound in water were also excluded as not directly relevant. It is believed that the approximately 400 titles included form 
a fairly exhaustive compilation of present knowledge of electromagnetic wave propagation through the troposphere. 

The reports are grouped and a Bibliography number has been assigned to each report. The letter to the right of the Bibliog¬ 
raphy number designates the present United States security classification. 

Requests for copies of the reports listed herein may be made by Bibliography number referring to this edition, but should 
be made through the proper channels. The Central Radio Bureau is the distributing agent for American reports in Great 
Britain and for propagation reports originating in Great Baddow, Chelmsford, England. All other British reports may be ob¬ 
tained from the British government department controlling the sources. 

The OSRD Liaison Office will, upon request, supply readers in the United States who are not in the Armed Services with 
all reports originating outside of the United States. They will supply Army and Navy units with all except JEIA-numbered 
reports. Requests for the latter should be directed to the Joint Electronics Information Agency, Munitions Building, Wash¬ 
ington, D.C. 

In general, application should be made to the NDRC Chairman’s Office for reports written by NDRC Divisions, Committees, 
or contractors, NDRC Section 6.1 being the present exception; to the Bureau of Ships for reports from Naval Research Lab¬ 
oratory, Navy Radio and Sound Laboratory, and all reports appearing in Section 20 of the Bibliography (Under-Water Sound 
Propagation); to the Office of the Chief Signal Officer for Signal Corps reports; to Inter-Service Radio Propagation Laboratory, 
Bureau of Standards for IRPL reports. Requests for case-numbered BTL reports should be sent to the Director of Research, 
Bell Telephone Laboratories, 463 West Street, New York, N. Y. 


CLASSIFICATION OF REPORTS 


1.000 Conferences and Progress Reports 
2.000 General Discussions 
3.000 Standard Atmosphere Propagation 
4.000 Non-Standard Atmosphere Propagation—Pure 
Theory 

5.000 Non-Standard Atmosphere Propagation — Experi¬ 
ment and Theory 
6.000 Propagation Experiments 
7.000 Meteorological Theory 
8.000 Meteorological Experiments 
9.000 Meteorological Equipment 


10.000 Radar Forecasting 

11.000 Atmospheric Absorption and Scattering 

12.000 Dielectric Constant and Loss Factor 

13.000 Reflection Coefficient 

14.000 Horizontal and Vertical Polarization 

15.000 Effect of Hills, Trees, Obstacles, etc. 

16.000 Transmission over Part Land-Part Sea 

17.000 Targets and Echoes 

18.000 Doppler Effect 

19.000 Communication (Tropospheric) 

20.000 Under-Water Sound Propagation 


LIST OF ABBREVIATIONS 
AMERICAN 


AMG-C. 

Applied Mathematics Group, Colum¬ 
bia University 

BTL. 

Bell Telephone Laboratories 

CBS. 

Columbia Broadcasting System 

CESL. 

Camp Evans Signal Laboratory 

CP. 

Committee on Propagation 

CUDWR. 

Columbia University, Division of War 
Research 

IRPL. 

Inter Service Radio Propagation Lab¬ 
oratory; National Bureau of Standards 

JEIA. 

Joint Electronics Information Agency 


MIT. 

Massachusetts Institute of Technology 

NATC. 

Naval Air Training Center, Corpus 
Christi, Texas 

NDRC. 

National Defense Research Committee 

NRL. 

Naval Research Laboratory 

NRSL. 

Navy Radio and Sound Laboratory 

OCSO. 

Office of the Chief Signal Officer 

OFS. 

Office of Field Service 

ORB. 

Operational Research Branch; 

Office of the Chief Signal Officer 


277 


278 


GENERAL BIBLIOGRAPHY 


ORG. 

Operational Research Group; 

GEC. 

General Electric Company 


Office of the Chief Signal Officer 

ICI. 

Imperial Chemical Industries 

RCA. 

Radio Corporation of America 

JIEE. 

Journal of the Institution of Electrical 

RL. 

Radiation Laboratory, M.I.T. 


Engineers 

RRL. 

Radio Research Laboratory, Harvard 
University 

JMRP. 

Joint Meteorological Radio Propaga¬ 
tion Sub-Committee 

SWP. 

South West Pacific 

MAP. 

Ministry of Aircraft Production 

TCAW. 

Technical Committee on Air Warn¬ 

MO. 

Meteorological Office, Air Ministry 


ing, Office of the Sec’y of War; 

MetResCom. 

Meteorological Research Committee 


Reports distributed by Radiation 

NMS. 

Naval Meteorological Service 


Laboratory 

NPL. 

National Physical Laboratory 

UCDWR. 

University of California, Division of 
War Research 

ORS-ADGB. 

Operational Research Section, Air De¬ 
fense of Great Britain 

WD, HQAAF. 

Weather Division, Headquarters Army 

POED. 

Post Office Engineering Department 


Air Forces 

RAE. 

Royal Aircraft Establishment 

WPG 

Wave Propagation Group 

RRB. 

Radio Research Board 


AORG. 

ATP. 

CSIR-RL. 

RAAF. 

A& AEE. 
AC. 

ADRDE. 

AORG. 

ASE. 

BAD. 

BCSO. 

BRL. 

CAEE. 

CRB. 

CVD-CL. 

DMO. 

DSIR. 


AUSTRALIAN 

Australian Operational Research 
Group 

Australian Technical Paper 
Council for Scientific and Industrial 
Research, Radiophysics Laboratory 
Royal Australian Air Force 

BRITISH 

Aircraft and Armament Experimental 
Establishment 

Advisory Council on Scientific Re¬ 
search and Technical Development 
Air Defense Research and Develop¬ 
ment Establishment 
Army Operational Research Group 
Admiralty Signal Establishment 
British Admiralty Delegation 
British Central Scientific Office 
Baddow Research Laboratory 
Coast Artillery Experimental Estab¬ 
lishment 

Central Radio Bureau 
Coordination of Valve Development 
Committee, Clarendon Laboratory 
Director of Meteorological Office 
Department of Scientific and Indus¬ 
trial Research 


RRDE. 

SDTM. 

SRDE. 

TRE. 

USWP. 

USWP-WC. 

ORS-WAC. 

CAORG. 

ORS-RNZAF. 

RDL-DSIR-NZ. 

ORS-SEA. 


Radar Research and Development 
Establishment 

Synoptic Divisions Technical Memo¬ 
randum 

Signal Research and Development 
Establishment 

Telecommunications Research Estab¬ 
lishment 

Ultra Short Wave Propagation Panel 
of the RDF Application Committee 
Ultra Short Wave Propagation Panel, 
Working Committee 

CANADIAN 

Operational Research Section, West¬ 
ern Air Command, Royal Canadian 
Air Force 

Canadian Army Operational Research 
Group 

NEW ZEALAND 

Operational Research Station, Royal 
N.Z. Air Force 

Radio Development Laboratory, De¬ 
partment of Scientific and Industrial 
Research—New Zealand 

SOUTH EAST ASIA 
Operational Research Section, South 
East Asia 


Author or Source Number Date 


1.000 CONFERENCES AND PROGRESS REPORTS 


1.001 S 

The Effect of the Atmosphere on the Propagation of 
Radio Waves. First Report on American Investiga¬ 
tions. 

H. G. Hopkins 

BCSO 

No. 201 

June 16 
1943 

1.002 S 

The Effect of the Atmosphere on the Propagation of 
Radio Waves. Second Report on American Investiga¬ 
tions. 

H. G. Hopkins 

BCSO 

No. 218 

Aug. 6 
1943 

1.003 C 

Notes on Microwave Propagation Conference at 
MIT Radiation Laboratory. 

RL 

RL 42- 

Sept. 24 
1943 

1.004 S 

Report on K-Band Work in U.S.A. 

B. Bleaney 

RL 475 

Oct. 20 

1.005 S 

Monthly Progress Report for the Month of March, 
1944 (New Zealand). 

RDL-DSIR 

NZ 

RD 1/363 

1943 
Apr. 14 

1944 







GENERAL BIBLIOGRAPHY 


279 


Bib. No. 

1.006 C 
1.007 C 
1.008 S 

1.009 S 

1.010 S 
1.011 S 
1.012 S 


Title Author or Source Number Date 

1.000 CONFERENCES AND PROGRESS REPORTS (continued) 


Report of International Radio Propagation Confer¬ 
ence. 

Conference on Propagation—February 10-11, 1944— 
Empire State Building, New York. 

TRE Progress Report for the Period 16th June to 
15th July, 1944. 

Progress Report, Radio Development Laboratory, 
DSIR, New Zealand for Months of June and July, 
1944. 

Scientific Investigations on Propagation Problems in 
the South West Pacific Area. 

The Air Defense System of the Near Islands. 

Reviews of Progress of USW Propagation Work, 

I The Evaluation of Solutions of the Wave Equation 
for a Stratified Medium. 

II Statement of Work in Progress Relevant to In¬ 
vestigations of the Propagation of Radio Waves 
Through the Troposphere. 

III Microwave Propagation Research at Signal Re¬ 
search & Development Establishment. 

IV Correlation of Radar Operational Data with 
Meteorological Conditions. 

V Progress Report on Forecasting of Radar Condi¬ 
tions. 

VI Vertical Temperature and Humidity Gradients at 
Rye. 

VII The Use of Radar for the Detection of Storms. 


VIII Present States of Theoretical Study of Radio 
Propagation Through the Troposphere by the Math¬ 
ematics Group. 

IX Review of Short-Period Experimental Studies of 
Centimetre Wave Propagation, Carried out Jointly 
by ASE, SRDE and GEC. 

X Study of Cm. Wave Propagation over Cardigan 
Bay to Mount Snowden. 

XI Study of Reflection Coefficient of the Sea at 
Centimetre Wavelengths. 

XII K, X, and S (LLANDUDNO) Trials—General 
Summary of the Experimental Results Obtained 
which are Concerned with the Dependence of Radio 
Propagation on Meteorological Conditions. 

XIII Progress Report on 369 Trials by DNMS. 


XIV Survey of Progress in the United Kingdom on 
the Electromagnetic Theory of Tropospheric Propa¬ 
gation. 


IRPL 

IRPL-C61 

June 

1944 

CUDWR 

CP 

1944 

WPG 

NDRC 


TRE 

MAP File 

June- 


Ref. No. SB 

July 


30917 

1944 

RDL-DSIR 

RD 1/439 

June- 

NZ 

or JEIA 

July 


5491 

1944 

F. W. G. White 

Australia 

July 25 
1944 

T. J. Carroll 

OCSO 

Aug. 30 

USWP 

OAD-55 

1944 

D. R. Hartree 

AC 7017/ 

Sept. 26 


RDF 239 or 
JEIA 593* 

1944 

R. L. Smith-Rose 

AC 7018/ 

Sept. 25 

(NPL) 

USW 

1944 

SRDE 

AC 7019/ 

Sept. 26 


USW 

or JEIA 6464 

1944 

AORG 

AC 7020/ 

Sept. 28 


USW 

or JEIA 6463 

1944 

DMO 

AC 7021/ 

Oct. 2 


USW 

or JEIA 6462 

1944 

DMO 

AC 7022/ 

Oct. 2 


USW 

or JEIA 6461 

1944 

DMO 

AC 7023/ 

Oct. 2 


USW 

or JEIA 6460 

1944 

TRE 

AC 7024/ 

Oct. 2 


USW 

or JEIA 6459 

1944 

E. C. S. Megaw 

AC 7025/ 

Oct. 16 

(GEC) 

USW 

or JEIA 6458 

1944 

F. Hoyle 

AC 7026/ 

Oct. 14 


USW 

1944 

F. Hoyle 

AC 7027/ 

Oct. 14 


USW 

1944 

TRE & 

AC 7028/ 

Oct. 14 

RRDE 

USW 

1944 


DNMS 

AC 7029/ 

Oct. 14 


RDF 240 

1944 


USW 



or JEIA 6466 


RRDE 

AC 7030/ 

Oct. 16 


USW 

1944 




280 


GENERAL BIBLIOGRAPHY 


Bib. No. Title Author or Source Number Date 

1.000 CONFERENCES AND PROGRESS REPORTS (continued) 



XV Study of Meteorological Factors Responsible for 

RRDE 

AC 7031/ 

Oct 16 


the Refractive Structure of the Troposphere. 


USW 

1944 

1.013 S 

Report No. 1 of Project SWP—3.2 of the OFS. 

P. A. Anderson 

Washington 

Nov. 2 



State Coll. 

1944 

1.014 C 

Data on Super Refraction Supplied by Australian 

J. W. Reed 

CSIR-RL 

Dec. 6 


Radar Stations. (Progress Report on Analysis of Data 
from 200 Mc/s. Radar Stations Mar.-Aug., 1944). 


RP 229/1 

1944 

1.015 S 

Report No. 2 of Project SWP—3.2 of the OFS. 

P. A. Anderson 

Washington 

Jan. 7 



State Coll. 

1945 

1.016 S 

Third Conference on Propagation—Washington, 

CUDWR-WPG 

CP 

1945 


D.C.—Nov. 16-18, 1944. 


NDRC 


1.017 R 

Survey of Field of Radio Propagation and Noise with 

F. J. Kerr 

CSIR RP 

Nov. 27 


Special Reference to Australia. 


231 or 

JEIA 8641 

1944 


2.000 GENERAL 

DISCUSSIONS 



2.001 S 

Considerations Affecting Choice of Wavelength. 

K. T. Bainbridge 

RL- 

Sept. 24 




V-7S 

1941 

2.002 S 

Notes on Microwaves. 

W. W. Hansen 

RL- 

Oct. 20 

• 



T-2 

1941 

2.003 S 

Fundamentals of Early Warning Radar. 

ORG 

OCSO 

Mar. 5 



ORG-E-5-1 

1943 

2.004 S 

RDF Propagation at Centimeter Wavelengths. 

F. J. Kerr 

Australia 

Apr. 27 




No. 284 

RP 177 

1943 

2.005 C 

Notes on Ultra Short Wave Propagation in the 

H. G. Booker 

TRE 

Aug. 9 


United States. 


S 4457 

1943 

2.006 C 

An Introduction to Microwave Propagation. 

D. E. Kerr 

RL 406 

Sept. 16 



P. Rubenstein 


1943 

2.007 R 

Electrical Communication Systems Engineering. 

War Dept. 

TM 11-486 a 

Feb. 25 

1944 

2nd Edition 
Apr. 25 

1945 

2.008 C 

Anomalous Propagation and the Army. 

T. J. Carroll 

OCSO 

Mar. 4 




Rep. No. 

1944 




ORB-P-18-1 


2.009 C 

Radar System Fundamentals. 

War Dept. 

TM 11-467 

Apr. 28 



- 


1944 

2.010 R 

Radio Fundamentals. 

War Dept. 

TM 11-455 

May 22 

1944 

2 011 R 

Radar Electronic Fundamentals. 

War Dept. 

TM 11-466 

June 29 

1944 

2.012 C 

Principles of Radar. 

Staff of MIT 

Radar School 


1944 

2.013 C 

Fundamentals of Radar. 

Staff of Radar 

NAVAER 08- 

Nov. 10 



Fund. Sec.- 
NATC 

5S-108 

1944 

2.014 

General Lecture Series on Radar Components. 

RL 

RL T-18 

Dec. 1, 1944 

2.015 C 

Radar Performance Testing Manual. 

HQ, AAF 

Air Forces 

July 1944 



Manual No. 28 

2nd Edition 

2.016 R 

Effects of Site Conditions on Operation of Ground 

J. L. Putman 

TRE 



Radar Installation on Aerodromes. See also 10.007. 


T 1805 



3.000 STANDARD ATMOSPHERE PROPAGATION 


3.001 

The Diffraction of Electro-magnetic Waves from an 

H. Bremmer 

Phil. Mag. 

July 


Electrical Point Source Round a Finitely Conducting 

Balth. Van Der Pol 

Vol. 24. 

1937 




GENERAL BIBLIOGRAPHY 281 


Bib. No. 

Title 

Author or Source 

Number 

Date 


3.000 STANDARD ATMOSPHERE 

PROPAGATION (continued) 



Sphere, with Applications to Radiotelegraphy and 
the Theory of the Rainbow. Part I 


pp 141-176 



The Diffraction of Electro-magnetic Waves from an 

H. Bremmer 

Phil. Mag. 

Supp. 


Electrical Point Source Round a Finitely Conducting 

Balth. Van Der Pol 

Vol. 24 

Nov. 


Sphere, with Applications to Radiotelegraphy and the 
Theory of the Rainbow. Part II 


pp 825-864 

1937 


The Propagation of Radio Waves over a Finitely 

H. Bremmer 

Phil. Mag. 

June 


Conducting Spherical Earth. Part III 

Balth. Van Der Pol 

Vol. 25 
pp 817-837 

1938 


Further Note on the Propagation of Radio Waves 

H. Bremmer 

Phil. Mag. 

March 


over a Finitely Conducting Spherical Earth. Part IV 

Balth. Van Der Pol 

Vol. 27 
pp 261-275 

1939 

3.002 

Ultra Short Wave Propagation Curves (0.1 to 10 

Marconi 

Marconi 

March 28 


Meters). 


Handbook 

1940 

3.003 

Report on Signal Strength Curves Within the Visual 

Marconi 

Marconi 

Nov. 


Range. 


RD 456 

1940 

3.004 

The Effect of the Earth’s Curvature on Ground-Wave 

C. R. Burrows 

Proc. IRE 

Jan. 


Propagation. 

M. C. Gray 

Vol. 29 
pp 16-24 

1941 

3.005 C 

The Siting of RDF Stations. Appendix: Screening of 

TRE 

TRE 

July 19 


RDF Sets from Fixed Echoes. 


T 1430 

1941 

3.006 R 

Propagation Curves for Wavelengths of 13 Meters. 

Marconi 

Marconi 

Nov. 


Supplement to USW Propagation Curves RD 456. 


Appendix 

RD 456A 

1941 

3.007 

The Calculation of Ground-Wave Field Intensity 

K. A. Norton 

Proc. IRE 

Dec. 


over a Finitely Conducting Spherical Earth. 


Vol. 29 
pp 623-639 

1941 

3.008 S 

Siting of Stations for Maximum Range. 

H. G. Booker 

TRE 

Feb. 9 




M/36 

1942 

3.009 S 

Microwave Interference Patterns. 

J. A. Stratton 

RL- 

Mar. 7 




C-l 

1942 

3.010 S 

Dependence of Range of Radar Equipment on Wave¬ 

C. R. Burrows 

BTL 

June 1 


length for ASV—Case 23815 and 23817. 


MM-42- 

160-54 

1942 

3.011 S 

Theoretical Field Strength of Ten Centimeter Equip¬ 

H. G. Booker 

TRE 

July 1 


ment over a Spherical Earth. 


M/45/HGB 

1942 

3.012 C 

Atmospheric Refraction and Height Determination 

E. Eastwood, F/O 

Calibration 

July 6 


by RDF. (Details and Results of a Numerical Meth¬ 

(RAF) 

Memo No. 54 

1942 


od of First Order Correction.) 


or JEIA 



(See 3.050) 


7773 


3.013 S 

Dependence of Range of Submarine Radar Equip¬ 

C. R. Burrows 

BTL 

July 9 


ment on Wavelength—Case 20564. 


MM-42- 

160-70 

1942 

3.014 S 

Transmission on 3000 Me. over Sea Water. 

J. A. Stratton 

RL- 

July 14 




C-2 

1942 

3.015 S 

Transmission on 100 Me. over Sea Water. 

J. A. Stratton 

RL- 

July 14 




C-3 

1942» 

3.016 S 

Transmission on 200 Me. over Sea Water. 

J. A. Stratton 

RL- 

July 14 




C-4 

1942 

3.017 S 

Transmission on 500 Me. over Sea Water. 

J. A. Stratton 

RL- 

July 14 




C-5 

1942 

3.018 C 

Interim Report on Propagation Within and Beyond 

C. Domb 

ASE 

Sept. 


the Optical Range. 

M. H. L. Pryce 

M 448 

1942 

3.019 C 

Theoretical Ground Ray Field Strengths and Height 

BRL 

BRL 

Sept 


Gain Curves for Wavelengths of 2—2000 M. 


Section E 

Tech. Rep. 383 

1942 

3.020 C 

Siting for Long Range Aircraft Detection. 

T. J. Carroll 

CESL 

Oct. 17 




No. T-13 

1942 (Rev.) 




282 GENERAL BIBLIOGRAPHY 


Bib. No. Title Author or Source Number Date 

3.000 STANDARD ATMOSPHERE PROPAGATION (continued) 


3.021 C 

YHF Field Strength Curves for Propagation within 

G. J. Camfield 

Radio/279 

Oct. 


the Line of Sight. 

RAE 

RAE Ref: 
Radio/s. 2111/ 
OPE 16 

1942 

3.022 S 

Relation of Radar Range to Frequency and Polar¬ 

J. A. Stratton 

RL- 

Nov. 3 


ization. 

R. A. Hutner 

C-6 

1942 

3.023 

1 to 10 Cm. Propagation Curves. 

G. Millington 

Marconi 

TR 460 

Jan. 

1943 

3.024 S 

Properties of the Diffracted Wave Field Intensity. 

R. A. Hutner 

E. Lyman 

RL- 

C-8 

Feb. 12 
1943 

3.025 S 

The Effect of Earth Curvature on the Performance 
Diagram of an RDF Station. 

TRE 

TRE 

29/R102/ 

LGHH 

Feb. 25 
1943 

3.026 S 

Radar Height Finding. 

R. A. Hutner 

H. Dodson 

J. Gill 

B. Howard 

F. Parker 

J. A. Stratton 

RL- 

C-9 

Apr. 6 
1943 

3.027 S 

Technical Requirements for GCI Search Systems. 

L. J. Chu 

TCAW 

May 10 


Technical Requirements for Early Warning Radar 
Systems. 

N. H. Frank 

RL 

1 and 2 

1943 

3.028 S 

Low-Angle Coverage of Early Warning Radar Sys¬ 
tems. 

N. H. Frank 

RL 

TCAW-3 

July 26 
1943 

3.029 S 

Factors Relating to the Design of an RDF Air Warn¬ 
ing Set. 

F. J. Kerr 

CSIR-RL 

RP 187 

Aug. 11 
1943 

3.030 C 

A Graphical Method of Computing the Bending of 
Radio Beams by the Effective Earth Radius Method. 

H. Raymond 

CESL 

No. T-14 

Aug. 27 
1943 

3.031 S 

Transmission at Low Altitudes over Sea Water. 

R. A. Hutner 

RL 

Sept. 1 



F. Parker 

B. Howard 

H. Dodson 

J. Gill 

C-10 

1943 

3.032 S 

Radio-Frequency Propagation Above the Earth’s 
Surface. 

P. F. Godley, Jr. 

RCA Lab. 

Rep. No. 

895-5 

Div. 15 
OEMsr-895 

Sept. 11 
1943 

3.033 S 

Field Intensity Formulas. 

R. A. Hutner 

H. Dodson 

J. Gill 

F. Parker 

B. Howard 

RL- 

C-ll 

Sept. 28 
1943 

3.034 R 

Propagation Curves. 

(See 3.046) 

BTL 

NDRC 

Div. 15 

966-6A 

Oct. 5 
1943 

3.035* 

Note on Field Intensity Computations for Elevated 
Antennas. Case 20878. 

M. C. Gray 

BTL 

MM-43- 

110-28 

Oct. 9 
1943 

3.036 C 

The Calculation of Expected Vertical Coverage Dia¬ 

M. Sherman 

CESL 

2/19/43 


grams. 

Revised by 

W. S. McAfee 

T-17 

Revision 

10/15/43 

3.037 R 

Charts for Use in Field Intensity Computations. 

K. Bullington 

NDRC 

Proj. C-79 

Nov. 2 
1943 

3.038 S 

Notes on Visibility Problems, Taking Account of the 

English 

AORG 

Dec. 1 


Curvature of the Earth. 

AORG 

No. 152 

1943 

3.039 C 

Simplified Methods of Field Intensity Calculations in 
the Interference Region. 

W. T. Fishback 

RL 461 

Dec. 8 
1943 






GENERAL BIBLIOGRAPHY 


283 


- 


Bib. No. 

Title 

Author or Source 

Number 

Date 


3.000 STANDARD ATMOSPHERE PROPAGATION (continued) 


3.040 C 

Field Strength Near and Beyond the Horizon for 

TRE 

TRE-M/ 

Dec. 24 


Wavelengths of Ten and Thirty Cms. 


Rep. 53/WW 

1943 

3.041 S 

Theoretical Field Strength Near and Beyond Horizon 

TRE 

TRE 

Feb. 24 


for Orthodox Propagation of Fifty Centimeter Waves. 


T 1635 

1944 

3.042 C 

Location of Signal Strength Maxima, Nulls, and Re¬ 

R. C. L. Timpson, 

First 

Apr. 7 


flection Areas for Standard U.S. Early Warning 
Radar Equipment. 

Major 

Air Force 

1944 

3.043 S 

Cover by German Coastal Radar on Low Flying Air¬ 

R. C. Raymond 

OCSO 

Apr. 15 


craft. 

I. H. Crowne 

OAD-25 

1944 

3.044 C 

The Propagation Functions for an Atmosphere with 

T. Pearcey 

RRDE 

Sept. 1 


Uniform Lapse-Rate of Refractive Index. 


Research 

Rep. No. 256 

1944 

3.045 S 

Ideal Field Intensity Distribution in the Vertical 

J. W. Herbstreit 

OCSO 

1944 


Plane for Transmitting or Receiving Antennas when 
Each has the Same Pattern. 


ORG-PP-5 


3.046 R 

Propagation Curves. 

BTL 

NDRC 

Oct. 


(Issue 3—Replacing Previous Issues.) 


Div. 15- 
Report 

966-6C 

1944 

3.047 C 

Field Strength Calculator for Vertical Coverage Pat¬ 

C. R. White 

CESL 

Dec. 20 


terns and Propagation Curves. 


Tech. Memo 

No. 154-E 

1944 

3.048 C 

b Theoretische Resultaten over de Voorplanting Van 

Balth. Van Der Pol 

Natuurkundig 

Aug. 


Radiogolven. 


Laboratorium 

1941 




N. V. Philips 

Trans. 




Gloeilampen 

Apr. 14 




Fabrieken, 

Eindhoven, 

Holland 

1945 

3.049 S 

Theory of the Vertical Field Patterns for RDF Sta¬ 

J. C. Jaeger 

CSIR-RL 

Mar. 17 


tions. 


RP 174 

1943 

3.050 

Height/Range/Alpha Tables (Tables Relating to the 

ORS 

ORS(ADGB) 

Aug. 10 


Height, Range and Angle of Elevation of an Air¬ 

ADGB 

Radar Memo 

1944 


craft.) 


No. 50 or 



(See 3.012.) 


JEIA-7766 


3.051 R 

The Calculation of Field Strength for Vertical Polar¬ 

A. M. Woodward 

TRE 



ization over Land and Sea on 20 to 80 Megacycles per 
Second. 


T 1704 


3.052 C 

Field Intensity Contours in Generalized Coordinates. 

H. Dodson 

RL 

May 2 



J. Gill 

702 

1945 



B. Howard 




4.000 NON-STANDARD ATMOSPHERE 

PROPAGATION-PURE THEORY 


4.001 S 

The Limiting Ranges of RDF Sets over the Sea. 

F. Hoyle 

ASE 

1943 



M. H. L. Pryce 

M 395 


4.002 S 

The Theory of Anomalous Propagation in the Tropo¬ 

H. G. Booker 

TRE 

Apr. 12 


sphere and Its Relation to Waveguides and Diffrac¬ 


M/60/HGB 

1943 


tion. 


or T 1447 


4.003 C 

The Tracing of Rays in the Refracting Atmosphere. 

T. Pearcey 

ADRDE 

Apr. 21 




AC 3878 

USW 

1943 

4.004 C 

Graphical Construction of a Radar Radiation Pattern 

L. Anderson 

NRSL 

May 1 


in a Stratified Atmosphere. 

F. R. Abbott 

WP-4 

1943 

4.005 S 

Improved Tropospheric Propagation—Curves Em¬ 

H. G. Booker 

TRE 

July 6 


bracing Anomalous Propagation. 


M/65/HGB 

1943 

4.006 C 

Radiation Patterns under Cases of Anomalous Prop¬ 

T. Pearcey 

ADRDE 

July 19 


agation. 


R 35 

1943 



284 


Bib. No. 

4.007 S 

4.008 C 

4.009 C 

4.010 C 
4.011 C 

4.012 C 
4.013 S 

4.014 C 
4.015 S 
4.016 S 

4.017 C 

4.018 S 
4.019 S 

4.020 S 

4.021 S 

4.022 S 
4.023 C 

4.024 C 

4.025 

4.026 C 
4.027 


GENERAL BIBLIOGRAPHY 


Title Author or Source Number Date 

4.000 NON-STANDARD ATMOSPHERE PROPAGATION—PURE THEORY (continued) 


Effect of Humidity Gradients in the Atmosphere on 
Propagation at RDF Frequencies. 

The Calculation of Field Strength Near the Surface 
of the Earth under Particular Conditions of Anom¬ 
alous Propagation. 

Anomalous Propagation over the Earth, Case 23703. 

The Effect of Atmospheric Refraction on Short Radio 
Waves. 

Radar Ray Patterns Associated with Normal and 
Anomalous Propagation Conditions. 

Transmission of Plane Waves Through a Single 
Stratum Separating Two Media. 

Notes on Theoretical Coverage Diagrams for Anom¬ 
alous Propagation. 

The Dependence of Microwave Propagation over Sea 
on the Structure of the Atmosphere. 

Improved Tropospheric Propagation—Curves Em¬ 
bracing Superrefraction. 

TRE Requirements for Propagation—Curves Em¬ 
bracing Superrefraction. 

The Mechanical Determination of the Path Differ¬ 
ence of Rays Subject to Discontinuities in the Verti¬ 
cal Gradient of Refractive Index. 

Improved Tropospheric Propagation—Curves Em¬ 
bracing Superrefraction. 

Interservice Propagation—Curves Embracing Super- 
refraction. Dependence of Mathematical Parameter 
L on Physical Entities. 

Theoretical Coverage-Diagrams for 10 Cm. Radars 
Embracing Superrefraction. 

Theoretical Coverage-Diagrams for 50 Cm. Radars 
Embracing Superrefraction. 

Theoretical Coverage of Navigational Aids Embrac¬ 
ing Superrefraction. 

The Theory of Propagation of Radio Waves in an 
Inhomogeneous Atmosphere (I). 

Reflection Coefficient of Layers of Varying Refrac¬ 
tive Index. 

Evaluation of the Solution of the Wave Equation for 
a Stratified Medium. (See 4.043.) 


Transmission of Plane Waves Through a Single Stra¬ 
tum Separating Two Media (II). 

Waves Guided by Dielectric Layers. 


Australian 

Oper. Res. 

July 28 

Operational 
Research Group 

Rep. No. 22 

1943 

T. Pearcey 

ADRDE 

Oct. 28 


Research 

Rep. No. 203 

1943 

S. A. Schelkunoff 

BTL 

Oct. 30 


MM-43-110 

33 

1943 

J. E. Freehafer 

RL 447 

Nov. 29 
1943 

F. P. Dane 

NRSL 

Dec. 10 

R. U. F. Hopkins 

L. J. Anderson 

WP-6 

1943 

J. B. Smyth 

NRSL 

Dec. 22 


WP-9 

1943 

TRE 

TRE 

Jan. 1 


TM/Memo/ 

14/AMW 

1944 

J. M. C. Scott 

ADRDE 

Feb. 4 

T. Pearcey 

Memo No. 40 

1944 

TRE 

TRE 

Feb. 18 


T 1625 

1944 

TRE 

TRE 

Feb. 25 


M/Memo 16/ 
HAB 

1944 

F. R. Abbott 

NRSL 

Mar. 10 

NRSL 

Rep. No. 

WP-10 

1944 

TRE 

TRE 

Mar. 28 


T 1626 

1944 

TRE 

TRE 

Apr. 3 


M/Memo 18/ 
WW 

1944 

TRE 

TRE 

Apr. 14 


T 1634 or 

JEIA 3229 

1944 

TRE 

TRE 

Apr. 14 


T 1659 or 

JEIA 3230 

1944 

TRE 

TRE 

Apr. 14 


T 1660 

1944 

T. Pearcey 

ADRDE 

April 


Research 

Rep. No. 245 

1944 

G. Millington 

BRL 

April 

BRL 

TR 483 or 

JEIA 4644 

1944 

D. R. Hartree 

ADRDE 

May 24 

P. Nicholson 

N. Eyres 

J. Howlett 

T. Pearcey 

MR 47 

1944 

J. B. Smyth 

NRSL 

June 23 


WP-13 

1944 

S. A. Schelkunoff 

BTL 

July 5 


MM-44- 

110-52 

1944 




GENERAL BIBLIOGRAPHY 


285 


Bib. No. 

4.028 C 

4.029 C 

4.030 R 
4.031 R 

4.032 C 
4.033 R 

4.034 R 

4.035 R 
4.036 C 
4.037 C 
4.038 C 

4.039 C 
4.040 C 
4.041 C 

4.042 C 
4.043 C 

4.044 R 
4.045 C 

4.046 C 
4.047 C 
4.048 C 

5.001 C 


Title Author or Source Number Date 

4.000 NON-STANDARD ATMOSPHERE PROPAGATION—PURE THEORY (continued) 


Microwave Transmission in Nonhomogeneous Atmos¬ 

S. A. Schelkunoff 

BTL 

July 5 

phere. 

\ 

MM-44- 

110-53 

1944 

Contour Diagrams of the Radiated Field of a Dipole 

T. Pearcey 

RRDE 

July 15 

under Various Conditions of Anomalous Propagation. 

F. Whitehead 

Research 

1944 

(See 4.045.) 


Report 

No. 257 


Theoretical Coverage-Diagrams for \y 2 Metre Ra¬ 

A. M. W. Woodward 

TRE 

July 23 

dars Embracing Superrefraction. 


T 1708 

1944 

Propagation Curves Embracing Superrefraction: SS 

H. G. Booker 

TRE 

Sept. 7 

Duct, Profile-Index 0.2 (Preliminary Edition). 


M/Memo 

23/WW 

1944 

A Note on the Reflection Coefficient of an Isotropic 

G. Millington 

BRL TR 497 

Oct. 5 

Layer of Varying Refractive Index. 

BRL 

or JEIA 6481 

1944 

Predicted Low Level Coverage of S-Band Shipborne 

F. R. Abbott 

NRSL 

Nov. 1 

Radars as Affected by Weather. (Horizontal Polar¬ 

L. L. Whittemore 

WP-14 

1944 

ization—Antenna Height 100 Ft.) 

L. W. Cross 

E. J. Wyrostek 



Predicted Low Level Coverage of 200 Mcs Band 

F. R. Abbott 

NRSL 

Nov. 4 

Shipborne Radars as Affected by Weather. (Hori¬ 

L. L. Whittemore 

WP-15 

1944 

zontal Polarization—Antenna Height 100 Feet.) 

L. W. Cross 

E. J. Wyrostek 



Variational Method for Determining Eigenvalues of 

G. G. Macfarlane 

TRE 

Nov. 13 

Wave Equation of Anomalous Propagation. 


T 1756 

1944 

Wave Propagation Analysis with the Aid of Non- 

B. Liebowitz 

CUDWR 

Dec. 

Euclidian Spaces. 


WPG-7 

1944 

Atmospheric Waves—Fluctuations in High Fre¬ 

L. G. Trolese 

NRSL 

Feb. 1 

quency Radio Waves. 

J. B. Smyth 

WP-18 

1945 

The Relation Between the Wave Equation and the 

T. L. Eckersley 

BRL TR-501 

Jan. 

Non-Linear First Order Equation of the Riccati 
Type. 


or JEIA 9104 

1945 

A Report on Transmission of Waves over the Earth. 

T. L. Eckersley 

BRL 

Jan. 



TR 504 

1945 

New Convergent Integrals. 

T. L. Eckersley 

BRL 

Feb. 



TR 509 

1945 

The Effect of a Subrefracting Layer of Atmosphere 

T. Pearcey 

RRDE Memo 

Feb. 12 

upon the Propagation of Radio Waves. 

M. Tomlin 

No. 83 or 
JEIA-8371 

1945 

Theory of Characteristic Functions in Problems of 

W. H. Furry 

RL 680 

Feb. 28 

Anomalous Propagation. 



1945 

The Evaluation of the Solution of the Wave Equation 

D. R. Hartree 

RRDE 

Mar. 12 

for a Stratified Medium (II). 


Res. Rep. 

1945 

(See 4.025.) 


No. 279 


Theoretical Coverage Diagrams for 3 Metre Radars 

W. Walkinshaw 

TRE T 1815 

Mar. 18 

Embracing Superrefraction. 

R. Hensman 

or JEIA 9198 

1945 

The Radiation Field of a Dipole under Various Con¬ 

T. Pearcey 

RRDE 

Apr. 13 

ditions of Anomalous Propagation. 

M. Tomlin 

Res. Rep. 

1945 

(See 4.029.) 

F. Whitehead 

No. 275 


Notes on the Solution of a Non-Linear First Order 

T. L. Eckersley 

BRL TR 502 

May 

Equation of the Riccati Type. (See 4.038.) 


or JEIA-9725 

1945 

Perturbation Theory for an Exponential M-curve in 

C. L. Pekeris 

CUDWR 

July 

Non-Standard Propagation. 


WPG-12 

1945 

c Graphs for Computing the Diffraction Field with 

P. J. Rubenstein 

RL 799 

Aug. 13 

Standard and Superstandard Refraction. 

W. T. Fishback 


1945 


5.000 NON-STANDARD ATMOSPHERE PROPAGATION—EXPERIMENT AND THEORY 
Radio Interpretation of Meteorological Observations TRE T 1471 1940 

in the First Two Meters of Atmosphere Above Grass TRE 

at Harlington, Middlesex, January to June, 1940. M/63 




286 


GENERAL BIBLIOGRAPHY 


Bib. No. 

Title 

Author or Source 

Number 

Date 

5.000 

NON-STANDARD ATMOSPHERE PROPAGATION-EXPERIMENT 

AND THEORY (continued) 

5.002 S 

Anomalous Echoes Observed with 10 Cms. CD Set. 

A. E. Kempton 

ADRDE Research Oct. 8 


# 


Rep. No. 119 

1941 

5.003 C 

Centimeter Wave Propagation over Sea Between 

F. Hoyle 

ASE 

June 12 


High Sites just within Optical Range. 

E. C. S. Megaw 

GEC 

1942 

5.004 C 

Centimeter Wave Propagation over Land, II. Meas¬ 

G. W. N. Cobbold 

SRDE 

Oct. 16 


urements within and beyond Optical Range. 

H. Archer-Thomson 

GEC 

1942 



E. C. S. Megaw 

AC 2917/ Com. 136 

5.005 C 

Radar Wave Propagation. 

L. Anderson 

NRSL 

Nov. 30 



J. B. Smyth 

F. R. Abbott 

R. Revelle 

WP-2 

1942 

5.006 C 

Very Short Wave Interception and DF 

T. L. Eckersley 

BRL TR 438 

1943 

5.007 C 

Anomalous Propagation of 10 Cm. RDF Waves over 

AORG 

AORG 

2/6/43 


the Sea, Also: First Supplement. 


No. 87 

Supplement 




7/26/43 

5.008 S 

Investigation of Propagation Characteristics of AW 

Australian 

Oper. Res. 

Mar. 9 


Stations. 

ORG 

Rep. No. 17 

1943 

5.009 

A Study of Propagation over the Ultra-Short-Wave 

R. L. Smith-Rose 

JIEE 

Mar. 


Radio Link between Guernsey and England on Wave¬ 

A. C. Stickland 

90 

1943 


lengths of 5 and 8 Meters (60 and 37.5 Mc/s.). 

NPL 



5.010 C 

The Effect of Atmospheric Refraction on the Propa¬ 

A. C. Stickland 

RRB 

Mar. 20 


gation of Radio Waves. 

NPL 

/S 10 

1943 

5.011 S 

Propagation of Ultra-Short Waves. 

H. C. Webster 

Australia 

Apr. 17 



Rep. No. 354 

1943 

5.012 C 

Report on Radar Wave Propagation. Atmospheric 

L. Anderson 

NRSL 

May 7 


Refraction—A Qualitative Investigation. 

J. B. Smyth 

WP-5 

1943 

5.013 C 

Radio Interpretation of Meteorological Observations 

TRE 

TRE M/61 

May 14 


in the First 400 Feet Above Cardington, 1942. 


or T 1413 

1943 

5.014 S 

Centimeter Wave Propagation over Sea, II. Measure¬ 

G. W. N. Cobbold 

GEC 

May 27 


ments from Shore Sites Near and Beyond Optical 

A. J. Jones 

No. 8180 

1943 


Range. 

H. A. Bonnett 

E. C. S. Megaw 





H. Archer-Thompson 




E. M. Hickin 



5.015 S 

Preliminary Observations on Radio Propagation at 6 

G. W. Gilman 

BTL 

June 12 


Centimeters Between Beer’s Hill, New Jersey, and 


MM-43- 

1943 


New York-Case 37003-4, File 36691-1. 


160-87 


5.016 C 

Some Observations of Anomalous Propagation. 

TRE 

TRE M/64 

July 6 




or T 1483 

1943 

5.017 S 

Application of Anomalous Propagation to Operation¬ 

H. G. Booker 

TRE M/66/HGB July 7 


al Problems at Home and Abroad. 


or T 1484 or 
JMRP No. 3 

1943 

5.018 C 

Propagation of Signals on 45.1, 474 and 2800 Me. 

G. S. Wickizer 

NDRC 

July 20 


from Empire State Building to Hauppauge and 

A. M. Braaten 

Proj. 423 

1943 


Riverhead, L.I., New York. 

RCA 

Rep. No. 1 


5.019 

Propagation of Ultra Short Waves. 

T. L. Eckersley 

Marconi 

Aug. 1 




TR/476 

1943 

5.020 S 

The “K” Effect in Anomalous Propagation of Ultra- 

F. Syer, 

Australia 

Aug. 10 


Short Waves. 

Flying Officer, 

No. 266 or 

1943 



RAAF 

JMRP No. 11 


5.021 C 

The Propagation of 10 Cm. Waves over Land Paths 

P. A. Anderson 

Wash. State 

Oct. 26 


of 14, 52, and 112 Miles. 

C. L. Barker 

Coll. Rep. 

1943 



K. E. Fitzsimmons 

No. 4 NDRC 




S. T. Stephenson 

PDRC-647 


5.022 S 

The Propagation of 1-Cm. Waves over the Sea as 

J. M. C. Scott 

ADRDE 

Nov. 11 


Deduced from Meteorological Measurements. 

T. Pearcey 

Res. Rep. 

No. 227 or 
JMRP No. 4 

1943 





GENERAL BIBLIOGRAPHY 


287 


Bib. No. 

Title 

Author or Source 

Number 

Date 

5.000 

NON-STANDARD ATMOSPHERE PROPAGATION—EXPERIMENT 

AND THEORY (continued) 

5.023 S 

Centimeter Wave Propagation over Land. A Pre¬ 
liminary Study of the Field Strength Records be¬ 
tween March and Sept., 1943. 

R. L. Smith-Rose 

A. C. Stickland 

NPL 

DSIR 

RRB/S 13 
or JMRP 

No. 10 

Nov. 15 
1943 

5.024 C 

The Propagation of 10 Cm. Waves over an Inland 
Lake. Correlation with Meteorological Soundings. 

P. A. Anderson 

K. E. Fitzsimmons 

S. T. Stephenson 

Wash. State 

Coll. Rep. 

No. 5 NDRC 
PDRC-647 

Nov. 16 
1943 

5.025 C 

Measurements of Radar Wave Refraction and Asso¬ 
ciated Meteorological Conditions. 

L. J. Anderson 

L. G. Trolese 

NRSL 

WP-7 

Dec. 10 
1943 

5.026 C 

Anomalous Propagation in India—Preliminary Re¬ 
port on Overland Transmission in Bengal. 

South East Asia 

ORS-SEA 

Rep. No. S 5 

Dec. 30 
1943 

5.027 S 

Atmospheric Physics—Summary of Investigations on 
Anomalous Propagation of Radar Signals Carried out 
by the Australian Operational Research Group Dur¬ 
ing 1942-43. 

D. F. Martyn 

Aust. Oper. 
Research 

Group 

1942- 

1943 

Summary 

5.028 S 

The Cause of Short Period Fluctuations in Centi¬ 
metre Wave Communication. 

J. M. C. Scott 

ADRDE 

Memo 42 

Mar. 8 
1944 

5.029 S 

Anomalous Propagation in the Persian Gulf. 

Naval Officer 
in Charge, 

Hormuz 

AC 5975/ 

USW 

Rec’d 
Mar. 20 
1944 

5.030 S 

Effect of Super-refraction on Surface Coverage on 
Enemy 50 Cm. and 80 Cm. Radar Sets. 

TRE 

TRE 

M/Memo 19 

April 

1944 

5.031 S 

K-X-S Experiments, News Letter No. 1. 

T. Gold 

ASE 

MK 12201 

May 3 
1944 

5.032 S 

Abnormal Radar Propagation in the South Pacific. 
An Investigation into Conditions in New Zealand and 
Norfolk Island on 200 Mc/s. with Notes on Fiji, New 
Caledonia and Solomon Islands. 

ORS-RNZAF 

Air Dept. 

Wellington 

RNAZAF 

Rep. No. 119 

File 135/ 

14/10 

May 4 
1944 

5.033 C 

Procedure and Charts for Estimating the Low Level 
Coverage of Shipborne 200 Mcs. Radars under Con¬ 
ditions of Pronounced Refraction. 

F. R. Abbott 

L. J. Anderson 

F. P. Dane 

J. P. Day 

R. U. F. Hopkins 

J. B. Smyth 

L. G. Trolese 

Ens. A. P. D. Stokes 

NRSL 

WP-11 (Rev.) 
BuShips 

Prob. No. 
X4-49CD 

May 10 

1944 

Revised 

5.034 S 

Centimeter Propagation over Land. A Study of the 
Field Strength Records Obtained During the Year 
1943-1944. 

A. C. Stickland DSIR 

(NPL) RRB/ 

Fit. Lt. R. W. Hatcher S 18 or 
(MO) JEIA 4789 

May 11 
1944 

5.035 S 

K-X-S Experiments, News Letter No. 2. 

T. Gold 

ASE 

MK 12201 

May 13 
1944 

5.036 C 

Atmospheric Propagation Effects and Relay Equip¬ 
ment. 

T. J. Carroll 

OCSO 

ORB-PP- 

12-1 

May 18 
1944 

5.037 C 

Low-Level Coverage of Radars as Affected by Weath¬ 
er. Procedures and Charts. (5.033 Reprinted.) 

NRSL 

IRPL 

T2a 

May 25 
1944 

5.038 R 

Variations in Radar Coverage. 

Earlier Editions have Appeared As: 

Joint Communi¬ 
cations Board 

JANP 101 

June 1 
1944 

R 

Radar Operation and Weather. 

CUDWR- 

WPG 

IRPL 

T-l 

May 

1944 

C 

Weather Influences in Radar Wave Propagation. 

CUDWR- 

WPG 

NAVAER 

50-IT-16 

May 

1944 

5.039 S 

Effect of Atmospheric Refraction on Range Measure¬ 
ments. 

G. G. Macfarlane 

TRE 

T 1688 

June 12 
1944 



288 


GENERAL BIBLIOGRAPHY 


Bib. No. Title Author or Source Number Date 


5.000 NON-STANDARD ATMOSPHERE PROPAGATION—EXPERIMENT AND THEORY (continued) 


5.040 C 

Microwave Transmission over Water and Land under 
Various Meteorological Conditions. 

P. J. Rubenstein 

I. Katz 

L. J. Neelands 

R. M. Mitchell 

RL 547 

June 13 
1944 

5.041 S 

Abnormal Propagation in WAC for May and June, 
1944. 

Canadian 

ORS-WAC 

Rep. 10 

July 27 
1944 

5.042 C 

Propagation of Signals on 45.1, 474 and 2800 Me. 
From Empire State Building, N. Y. C. to Hauppauge 
and Riverhead, L. I., N. Y. 

G. S. Wickizer 

A. M. Braaten 
(RCA) 

NDRC 

Proj. 423 

Rep. No. 2 

July 31 
1944 

5.043 C 

The Structure of the Electromagnetic Field During 
Conditions of Anomalous Propagation. 

T. Pearcey 

F. Whitehead 

RRDE 

Res. Rep. 

No. 258 

Sept. 19 
1944 

5.044 C 

Tropospheric Propagation and Radio-Meteorology. 

CUDWR- 

WPG 

CUDWR 

WPG-5 

Sept. 

1944 

5.045 C 

Some Factors Causing “Superrefraction” on Ultra 
High Frequencies in South West Pacific. (Daily Re¬ 
port on Abnormal Echoes—RAAF. Form No. 146 
Included in ATP 821.) 

D. F. Martyn 

F/Lt. P. Squires 

Australian 

Ionosphere 

Bui. Sect. 1.2 
or ATP 821 

Oct. 

1944 

5.046 

Aeroplane Tests. 

BRL 

JMRP No. 35 
or BRL 

TR 488-A 

Dec. 21 
1944 

5.047 C 

Atmospheric Refraction—A Preliminary Qualitative 
Investigation. 

L. J. Anderson 

F. P. Dane 

J. P. Day 

R. F. Hopkins 

L. G. Trolese 

Lt. A. P. D. Stokes 

NRSL 

WP-17 

Dec. 28 
1944 

5.048 S 

Anomalous Propagation with High and Low Sited 3 
cm. Ship Watching Radar Sets. 

G. C. Varley 

AORG 

Rep. No. 250 

Mar. 20 
1945 

5.049 S 

d Anomalous Propagation at English Coastal Radar 
Stations, March-September, 1944. 

6.000 PROPAGATION 

D. Lack 

EXPERIMENTS 

AORG 

Rep. No. 258 
or JEIA 9946 

May 30 
1945 

6.001 

Lebanon-Beer’s Hill Transmission on Wavelengths of 
2.0 Meters and 30 Centimeters—Case 20564. 

A. B. Crawford 

BTL 

MM-39- 

326-98 

Dec. 5 
1939 

6.002 C 

Centimeter Wave Propagation over Land: Prelimi¬ 
nary Trials. 

G. W. N. Cobbold 

H. A. Bonnett 

A. J. Jones 

E. C. S. Megaw 

H. Archer-Thomson 
A. S. Gladwin 

E. M. Hickin 

GEC 

No. 8045 

Aug. 21 
1942 

6.003 C 

The Propagation of 10 Cm. Waves on a 52-Mile Opti¬ 
cal Path over Land. The Correlation of Signal Pat¬ 
terns amd Radiosonde Data. 

P. A. Anderson 

C. L. Barker 

S. T. Stephenson 

K. E. Fitzsimmons 

Washington 

State Coll. 

Rep. No. 1 

NDRC-PDRC- 

647 

June 10 
1943 

6.004 C 

Centimeter Wave Propagation over Sea Within and 
Beyond the Optical Range. 

E. C. S. Megaw 

H. Archer-Thomson 

E. M. Hickin 

F. Hoyle 

ASE 

M 532 

July 

1943 

6.005 S 

Aden-Berbera VHF Experiments—Final Report on 
Propagation Aspects. 

Lt. E. W. Walker 

Lt. S. R. Bickerdike 

SRDE 

MS 4 

Dec. '42 
July ’43 



GENERAL BIBLIOGRAPHY 


289 


Bib. No. Title Author or Source Number 


6.000 PROPAGATION EXPERIMENTS (continued) 


6.006 S 

Investigation No. 369 (Irish Sea Experiment). 

British 

Min. of Supply 

AC 5970 

AC 5971 

AC 5972 

AC 5973 

AC 5974 

AC 6334 

AC 6828 

AC 7206 

AC 7465 

AC 7668 

6.007 S 

Experience with Space and Frequency Diversity Fad¬ 
ing on New York-Neshanic Microwave Circuit— 
Case 37003-4. 

G. W. Gilman 

F. H. Willis 

BTL 

MM-43- 

160-152 

6.008 C 

Investigation of Changes in Direction of Transmis¬ 
sion during Periods of Fading in the Microwave 
Range—Case 37003-4, File 36691-1. 

A. C. Peterson 

BTL 

MM-43- 

160-183 

6.009 C 

Radar Calibration Report—New York Region. 

Maj. R. C. L. 
Timpson 

Mitchell 

Field, N. Y. 

6.010 S 

Aden-Berbera YHF Experiments—Meteorological 
Conditions and Possible Correlations. 

Lt. E. W. Walker 

SRDE 

AC 5493/ 

USW 

or JMRP No. 14 

6.011 S 

Propagation Measurements on Polo Pony R/T 
Equipment. 

TRE 

TRE 

T 1609 

6.012 C 

Propagation over Short Paths and Rough Terrain at 
200 Mc/s. 

A. B. Vane 

D. G. Wilson 

RL 468 

6.013 S 

Propagation and Reflection Characteristics of Radio 
Waves as Affecting Radar. 

Lt. W. G. Michels 
Lt. W. C. Pomeroy 

Army Air 

Forces 

Board 

Proj. No. 

(M-3) 11a 

6.014 S 

Microwave Propagation Measurements—Report Pre¬ 
sented at NDRC Conference of Feb. 10-11, 1944. 

F. H. Willis 

BTL 

MM-44- 

160-55 

6.015 S 

Army Air Force Cold Weather Tests, Fairbanks, 
Alaska, Winter 1943-1944. 

R. W. Griffiths 

Western 

Elec. Co. 

6.016 S 

An Ultra-Short-Wave Field, Array Polar Diagram, 
and DF Survey (North Devon and Cornwall—Sept.- 
Oct., 1943). 

D. A. Thorn 

W. J. Bray 

J. H. H. Merriman 

R. J. Harris 

S. D. Whiddett 

H. Prain 

POED 

RR No. 

1141 

6.017 C 

An Estimation of the Incidence of Anomalous Propa¬ 
gation in the Cook Strait Area of New Zealand from 
Jan., 1943 to Jan., 1944. 

F. E. S. Alexander 

RDL-DSIR 

NZ 

RD 

1/373 

6.018 S 

K-Band Radar Transmission—A Preliminary Report 
of Tests Made Near Atlantic Highlands, N. J., be¬ 
tween December, 1943 and April, 1944. 

G. C. Southworth 

A. P. King 

S. D. Robertson 

BTL 

MM-44- 

160-115 

6.019 S 

Effect of Pulse Length on System Performance and 
Operation. 

R. Rollefson 

A. H. Nelson 

L. A. Hartman 

RL 571 

6.020 S 

Report on Cross Channel Propagation of British No. 
10 Set. 

K. R. Spangenberg 

OCSO 

OAB-2 


Date 


9/1/43 

12/14/43 

1/15/44 

2/9/44 

3/20/44 

5/14/44 

8/12/44 

10/19/44 

11/10/44 

1/4/45 

Sept. 18 
1943 


Oct. 30 
1943 


Nov. 30 
1943 

Dec. 20 
1943 


Dec. 31 

1943 

Jan. 18 

1944 

Jan. 31 
1944 


Mar. 10 
1944 

Apr. 20 
1944 

Apr. 29 
1944 


May 2 
1944 


May 19 
1944 


May 30 
1944 


Aug. 26 
1944 



290 


GENERAL BIBLIOGRAPHY 


Bib. No. Title Author or Source Number 


6.000 PROPAGATION EXPERIMENTS (continued) 


6.021 C 

Radar Range and Signal Strength. 

L. Jofey 

A. C. Cossor, Ltd. 
Res. Dept., 

Myra Works 

London E10 

MR 142 

6.022 C 

Results of Microwave Propagation Tests on the New 
York-Neshanic Path—Case 37003-4, File 36691-1. 

A. L. Durkee 

BTL 

MM-44- 

160-190 

6.023 C 

Height-Gain Tests in the Troposphere 

G. A. Isted 
(BRL) 

BRL TR 488 
or JEIA 5560 
or JMRP No. 36 

6.024 S 

Interim Report on Investigation of 120 Mc/s. and 50 
cm. Propagation Across the English Channel. 

W. R. Piggott 

AC 7081/ 

USW 

6.025 C 

Measurements of the Angle of Arrival of Microwaves 
in the X-Band (Case 20564). 

W. M. Sharpless 

BTL-MM- 

44-160-249 

6.026 C 

Over-Water Transmission Measurements, 1944— 
Part I: Preliminary Analysis of Radio and Radar 
Measurements. 

P. J. Rubenstein 

RL 649 

6.027 S 

The Vertical Distribution of Field Strength over the 
Sea Under Conditions of Normal and Anomalous 
Propagation. 

Maj. J. A. Ramsay 
CAEE & RRDE 

P. B. Blow (CAEE) 

RRDE 

Res. Rep. 

No. 267 

6.028 C 

Centimetre Wave Propagation over Sea. A Study of 
Signal Strength Records Taken in Cardigan Bay, 
Wales, between February and September, 1944. 

R. L. Smith-Rose 

A. C. Stickland 
(NPL) 

DSIR RRB/ 

C 114 or 

JMRP 

No. 50 

6.029 S 

Over-Water Tests on S-Band Early Warning for 
Ships. Vertical Coverage of the CXHR (SCI) Search 
System. 

W. O. Gordey 

D. T. Drake 

M. Kessler 

RL 703 

6.030 S 

Preliminary Report on S- and X-Band Propagation 
in Low Ducts Formed in Oceanic Air. 

M. Katzin 

NRL R-2493 

6.031 C 

Atmospheric Refraction under Conditions of a Radi¬ 
ation Inversion. 

L. J. Anderson 

J. P. Day 

C. H. Freres 

R. U. F. Hopkins 

J. B. Smyth 

Lt. A. P. D. Stokes 

NRSL 

WP-19 

6.032 R 

Radio-Meteorological Relationships. 

E. C. S. Megaw 

F. L. Westwater 

AC 8140/ 
USW138 

6.033 S 

Calculated Relationship Between Signal Level and 
Uniform Gradient of Refractive Index for the Irish 
Sea Paths. 

E. C. S. Megaw 
(GEC) 

GEC No. 8656 
AC 8225/ 

USW 141 

6.034 R 

Radio-Meteorological Relationships. General Sum¬ 
mary of Papers AC 8140/USW 138 and AC 8225/ 
USW 141. 

E. C. S. Megaw 

F. L. Westwater 

AC 8336/ 

USW 149 

6.035 C 

General Summary Covering the Work of the KXS 
Inter-Service Trials, LLANDUDNO, 1944. 

J. R. Atkinson 

TRE T1770 
JMRP No. 64 

6.036 S 

X-Band Trials at Rosehearty. 

J. R. Atkinson 

AC 8228/ 

USW 142 

JEIA 10401 

6.037 C 

e S- and X-Band Propagation in Low Ocean Ducts. R. W. Bauchman, Lt. 

(See 6.030.) W. Binnian, Lt. 

7.000 METEOROLOGICAL THEORY 

NRL R-2565 

7.001 C 

The Diffusive Properties of the Lower Atmosphere. 

O. G. Sutton 
Chemical Defense 
Experimental 

Station 

MRP 59 

Air Min. 

Met. Res. Com. 


Date 


Aug. 

1944 


Aug. 28 
1944 

Sept. 

1944 

Oct. 4 
1944 
Nov. 7 
1944 
Dec. 15 

1944 

Jan. 5 

1945 

Feb. 28 
1945 


Mar. 5 
1945 

Mar. 24 
1945 
Apr. 21 
1945 


May 4 
1945 
Apr. 19 
1945 

1945 


May 
1945 
May 28 
1945 

July 5 
1945 


Dec. 29 
1942 



GENERAL BIBLIOGRAPHY 


291 


Bib. No. Title Author or Source Number Date 

7.000 METEOROLOGICAL THEORY (continued) 


7.002 

Meteorology for Pilots. 

B. C. Haynes 

U.S. Dept. 

Jan. 




Commerce— 

Civil Aero. 

Bui. No. 25 

1943 

7.003 R 

A Study of the Effect of the Meteorology on the Re¬ 

H. Raymond 

CESL T-2 

May 4 


fraction of Radio Beams. 



1943 

7.004 R 

The Rapid Reduction of Meteorological Data to In¬ 

L. J. Anderson 

NRSL 

Dec. 10 


dex of Refraction. 

F. R. Abbott 

WP-8 

1943 

7.005 S 

Application of Diffusion Theory to Radio Refraction 

P. M. Woodward 

TRE 

Apr. 6 


Caused by Advection. 


T 1647 

1944 

7.006 C 

Qualitative Survey of Meteorological Factors Affect¬ 

I. Katz 

RL 488 

June 1 


ing Microwave Propagation. 

J. M. Austin 


1944 

7.007 

Suggested Programme of Observational Investigation 

H. G. Booker 

TRE 

July 29 


into Profiles in the Lower Atmosphere (HQ Air Com¬ 
mand, SE Asia, New Delhi). 

(TRE) 

S No. 9831 

1944 

7.008 R 

Analysis of Meteorological Ascents off New England. 

TRE 

Preliminary 

Sept. 7 




TRE 

M/Memo 22/ 
RAF 

1944 



R. A. Finlayson 

Revised 

TRE 

T 1774 or 

JMRP No. 54 

1945 

7.009 C 

The Influence of Ground Contour on Air Flow 

P. Queney 

CUDWR 

Sept. 


(Translation). 

Translated by 

W. M. Elsasser 

WPG-4 

1944 

7.010 R 

Radio-Meteorological Tables. 

TRE 

TRE 

T 1724 or 

JMRP No. 30 


7.011 C 

Modified Index Distribution Close to the Ocean Sur¬ 

R. B. Montgomery 

RL 651 

Feb. 16 


face. 

R. H. Burgoyne 


1945 

7.012 R 

Report of an Investigation of Subsidence in the Free 

Sverre Petterssen 

SDTM 

Sept. 29 


Atmosphere. 

P. A. Sheppard 

94 or 

1944 



C. H. B. Priestley 

JMRP 




K. R. Johanssen 

No. 49 


7.013 R 

The Influence of Atmospheric Stability on Air Flow. 

Lt. Commander 

AC 7892/ 

Mar. 7 



F. L. Westwater 

USW 126 
or JMRP No. 57 
or JEIA 10395 

1945 

7.014 

The Slopes of Isopycnic Surfaces in the Lower Atmos¬ 

Met. Office 

JMRP 

Mar. 29 


phere. 

Air Ministry 

No. 48 

1945 

7.015 C 

Tables for Computing the Modified Index of Refrac¬ 

E. R. Wicher 

CUDWR 

March 


tion M. 


WPG-8 

1945 

7.016 R 

Nomograms for Computation of Modified Index of 

R. H. Burgoyne 

NDRC 

Apr. 6 


Refraction. 


Div. 14 

RL 551 

1945 

7.017 

Note on Errors in Measurement of the Refractive 

G. A. Bull 

JMRP 

April 


Index of the Air for High Frequency Radio Waves 
Consequent upon Errors in Meteorological Measure¬ 


No. 51 

1945 


ments. 

Addendum: 

Note on Errors in Evaluation of Refractive Index of 

K. Stormonth 

Addendum 



the Air for Ultra-Short Radio Waves from the Data 


JMRP 



Obtained on the Rye Tower. 


No. 51 




292 


GENERAL BIBLIOGRAPHY 


Bib. No. Title Author or Source Number Date 

8.000 METEOROLOGICAL EXPERIMENTS 


8.001 

Weather in the Indian Ocean to Latitude 30° S. and 

MO 

MO 

1940 


Longitude 95° E. including the Red Sea and Persian 
Gulf. 


451b (7) 


8.002 

Weather on the Australia Station. 


RAAF 

July ’42 




Publication 

Reprinted 




No. 252 

Vol. II 

Sept. ’43 

8.003 S 

Note on the Hydrolapse in the First 1000 Ft. of the 

W. C. Swinbank 

MO 

July 12 


Atmosphere. 


SDTM 

No. 52 

1943 

8.004 S 

Meteorological Report in Connection with VHF 

Squadron 

AC 5492/ 

Oct. 30 


Wireless Experiment Between Aden and Berbera 

Leader 

USW 

1943 


(1943). 

Frith 

or JMRP 

No. 13 


8.005 

Meteorological Measurements (Irish Sea Experi¬ 

Inter-Service 




ments). 

Cm. Wave Prop. 
Research 

NMS 




Ship Glen Strathallan. 


S JEIA-2778 

11/1-5/43 




S HM 3/44 

1/14-17/44 




S JEIA-3059 

3/5-8/44 




C JEIA-3522 

3/14-16/44 




C JEIA-3520 

3/17-18/44 




S JEIA-3607 

3/22-25/44 




C JEIA-3523 

3/27-29/44 




S HM 3/44 

4/3-4/44 




S JEIA-3864 

4/10-13/44 




C JEIA-4123 

4/21-23/44 




C JEIA-4284 

4/27-30/44 




C JEIA-4729 

5/6-10/44 




C HM 3/44 

5/28-31/44 




C JEIA-5533 

6/21-7/7/44 




C HM 3/44 

7/17-22/44 




C JEIA-6185 

7/24-28/44 




C HM 3/44 

8/10-13/44 




C HM 3/44 

8/26-30/44 




C JEIA-6875 

10/6-10/44 




C JEIA-7309 

10/22-23/44 




C JEIA-8522 

7/11-14/44 


Ship Coila. 


C JEIA-3521 

12/15/43 




C JEIA-5207 

6/17-20/44 




C JEIA-5525 

6/9-27/44 




C JEIA-6850 

7/11-20/44 




C JEIA-6874 

10/10-11/44 




C JEIA-7307 

10/25-26/44 




C*JEIA-8521 

7/3-6/44 


Ship St. Dominica. 


C JEIA-4730 

5/19-30/44 




C JEIA-4915 

6/1-5/44 




C JEIA-6438 

7/24-27/44 




C HM 3/44 

8/19-21/44 




C HM 3/44 

8/26-29/44 




C*JEIA-8257 

7/30-8/2/44 

8.006 

Tables of Temperature and Humidity Observations 

MO 

JMRP 

Nov. 


at Rye. 


No. 5 

1943 

8.007 S 

Meteorological Information from Radar Stations 

Australian 

Australia 

Dec. 7 


being Circular Issued to RDF Stations and Fighter 


No. 405 or 

1943 


Sectors. 


JMRP No. 12 




GENERAL BIBLIOGRAPHY 


293 


Bib. No. Title Author or Source Number Date 

8.000 METEOROLOGICAL EXPERIMENTS (continued) 


8.008 R 

Low Altitude Measurements in New England to 

R. H. Burgoyne 

RL Rep. 

Feb. 22 


Determine Refractive Index—1943. 

I. Katz 

42-2/22/44 

1944 

8.009 S 

Climate in Relation to Microwave Radar Propaga¬ 
tion in Panama. 

A. E. Bent 

RL 476 

Feb. 25 
1944 

8.010 S 

The Vertical Distribution of Temperature and Hu¬ 
midity at Rye on the*Night of January 14-15, 1944. 

MO 

JMRP No. 6 or 
JEIA 10318 

Feb. 26 
1944 

8.011 S 

Analysis of Temperature and Humidity Records at 
Rye. 

MO 

JMRP No. 7 or 
JEIA 10319 

Feb. 

1944 

8.012 S 

Radio Climatology of the Persian Gulf and Gulf of 
Oman with Radar Confirmation. 

H. G. Booker 

TRE 

T 1642 

Mar. 15 
1944 

8.013 R 

Stations in the Western Hemisphere with Conditions 
in the Lower Layers of the Atmosphere Similar to 
Those at Selected Stations in the Eastern Hemi¬ 
sphere. 

Weather Div. 

HQ, AAF 

Rep. No. 729 

March 

1944 

8.014 C 

Rain Cloud Weather Reports Associated with the 

A. J. Oliver, 

6th Weather 

April 


Frontal Passage of 17-20 December, 1943. 

Sergeant, AC 

Region Res. 
Section 

APO No. 825 

1944 

8.015 

Some Extracts from Rye Records during April-May, 
1944. 

MO 

JMRP No. 20 
or JEIA 10321 

Apr.-May 

1944 

8.016 

Extract from Rye Records of Temperature and Hu¬ 
midity Gradients during Selected Radiation Nights, 
March, 1944. 

MO 

JMRP No. 18 
or JEIA 10320 

May 4 
1944 

8.017 

Some Values of the Refractive Index of the Atmos¬ 
phere at Rye. 

MO 8 

S 100958 or 
JMRP No. 23 
or JEIA 10322 

June 1-6 
1944 

8.018 C 

Low-Level Meteorological Soundings and Radar Cor¬ 

K. E. Fitzsimmons 

Wash. State 

June 12 


relation for the Panama Canal Zone. 

f 

S. T. Stephenson 

R. W. Bauchman 

Coll. Rep. 

No. 6 NDRC 
PDRC-647 

1944 

8.019 C 

Wave Propagation Report No. 3. 

Naval Res. Group 
Canal Zone 

Intel. Br. 

OCSO Canal 

Zone 413.44/ 

R113 

July 1 
1944 

8.020 S 

KXS Inter-Service Trials at LLANDUDNO Report 
of Colloquium held on June 27 & 28 at ADRDE, 
LLANDUDNO to Discuss the Results of the Trials 
up till that Date and to Define the Future Pro¬ 
gramme. 

ADRDE 

Part I 

Aug. 31 
1944 


Minutes of a Meeting of the Radar Section of an 
Inter-Service Conference held at LLANDUDNO on 
June 28, 1944—Appendix with Figures. Appendix I, 

II, III. 

ADRDE 

Part II 

Aug. 31 
1944 


Minutes of a Meeting of the Meteorological Section 
of an Inter-Service Conference held at ADRDE, 
LLANDUDNO, June 28, 1944. 

ADRDE 

Part III 

July 10 
1944 

8.021 C 

Preliminary Analysis of Height-Gain Tests in the 
Troposphere. 

R. F. C. McDowell 

BRL TR 494 
or JEIA 5777 

Sept. 

1944 

8.022 

Diurnal Variation of Temperature and Humidity at 
Various Heights at Rye. 

MO 8 

S 100958 or 

JMRP No. 26 or 
JEIA 10323 

Oct. 21 
1944 

8.023 C 

Report on General Climatic & Meteorological Condi¬ 

Directorate of 

RAAF 

Nov. 


tions in Banda Sea. (4°—7° S., 126°—131° E.) 

Meteorological 

Services 

Met. Res. 

Rep. List 

1944 


No. 2 Sect. II 
Series 7 No. 18 



294 


GENERAL BIBLIOGRAPHY 


Bib. No. Title Author or Source Number 


8.000 METEOROLOGICAL EXPERIMENTS (continued) 


8.024 

Hourly Values of Modified Refractive Index (M) for 
Meteorological Office, Rye, May, 1944. 

MO 

JMRP 

No. 31 or 

JEIA 10325 

8.025 C 

Temperature and Humidity Measurements Made 
with the Washington State College Wired Sonde 
Equipment at Kaikoura, New Zealand, Between 
Sept. 22, 1944 and Oct. 19, 1944. 

F. E. S. Alexander 

RDL-DSIR 

NZ 

RD 1/482 

8.026 C 

Fleet Weather Central Paper No. 10. Part I: High¬ 
lights of the December, 1944 Typhoon Including 
Photographic Radar Observations. Part II: A Distant 
Observation of a Warm Front Including a Photo¬ 
graph of Cloud Forms and Slope of Front. 

G. F. Kosco, 

Cmdr., USN 

Fleet 

Weather 

Central 

Paper No. 10 

8.027 C 

Results of Low Level Atmospheric Soundings in the 
Southwest and Central Pacific Oceanic Areas. 

P. A. Anderson 

K. E. Fitzsimmons 
G. M. Grover 

S. T. Stephenson 

Wash. State 
Coll. Rep. 

No. 9 NDRC 
PDRC-647 

8.028 C 

f Centimetre Wave Propagation over Sea. Correlation R. L. Smith-Rose 

of Radio Field Strength Transmitted Across Cardigan A. C. Stickland 

Bay, Wales with Gradient of Refractive Index Ob¬ 
tained from Aircraft Observations. 

9.000 METEOROLOGICAL EQUIPMENT 

DSIR RRB/ 
C121 or 

JEIA 9813 

9.001 

Brief Comparison of Air Temperature Thermometers 
Used and Tested at A & AEE For Meteorological 
Work. 

R. M. Goody 

A& AEE 

MRP 117 

9.002 C 

Project for Making Gee Meteorological Observations 
on Certain CH Towers. 

TRE 

TRE 

M/Memo/2 

9.003 S 

Balloon Psychrometer for the Measurement of the 
Relative Humidity of the Atmosphere at Various 
Heights. Also Addendum. 

S. M. Doble 
Addendum: 

S. M. Doble 

S. Inglefield 

ICI 

9.004 

A Distant Reading Electrical Air Temperature Ther¬ 
mometer Employing a Balanced Bridge Suitable for 
Use in Aircraft. 

A. W. Brewer 

MO 

MRP 112 

9.005 

The Cambridge Aircraft Electrical Resistance Ther¬ 
mometer—Notes on Its Use. 

A. W. Brewer 

MO 

MRP 113 

9.006 S 

Measurement of Atmospheric Humidity in Aircraft 
by Dew-Point Hygrometer. 

G. M. B. Dobson 

A. W. Brewer 

B. Cwilong 

MO 

MRP 126 

9.007 C 

The Captive Radiosonde and Wired Sonde Tech¬ 
niques for Detailed Low-Level Meteorological 
Sounding. 

P. A. Anderson 

C. L. Barker 

K. E. Fitzsimmons 
S. T. Stephenson 

Washington 
State Coll. 

Rep. No. 3 

NDRC- 

PDRC-647 

9.008 C 

A Comparison of Three Types of Cup Anemometer 
at Low Velocities. 

R. G. Dickinson 

H. S. Johnston 

NDRC-Div. 10 
Informal 

Rep. No. 
10.3A-38 

9.009 C 

A Remote Indicating Cup Anemometer with Mag¬ 
netic Coupling. 

R. G. Dickinson 

D. L. Kraus 

NDRC-Div. 10 
OSRD 

Rep. No. 3714 

9.010 C 

An Apparatus for Temperature Profile Measurement. 

R. G. Dickinson 

R. L. Mills 

H. S. Johnston 

NDRC 

Div. 10 
Informal 


Rep. No. 10.3A- 
45 


Date 


Dec. 28 

1944 

Jan. 15 

1945 


Feb. 10 
1944 


Feb. 27 
1945 


May 10 
1945 


Jan. 3 
1943 

Apr. 1, ’43 
Addendum 
Sept. 25, ’43 

June 21 
1943 

June 21 
1943 
Aug. 12 
1943 

Oct. 4 
1943 


Oct. 26 
1943 


Apr. 10 
1944 

Apr. 11 
1944 



GENERAL BIBLIOGRAPHY 


295 


Bib. No. Title Author or Source Number Date 

9.000 METEOROLOGICAL EQUIPMENT (continued) 


9.011 R 

Instruments and Methods for Measuring Tempera¬ 
ture and Humidity in the Lower Atmosphere. 

I. Katz 

RL 487 

Apr. 12 
1944 

9.012 C 

Anomalous Propagation—Adaptation of Model 
RAU-2 Radio Sonde Receiving and Recording 
Equipment for Use as Low Level Sounding Device. 

Friez Instrument 
Div.—Bendix 
Aviation Corp. 

Navy Dev. 
Project 

Unit No. 1 

May 31 
1944 

9.013 R 

Meteorological Investigation at Rye—Part I—In¬ 
strumental Layout for Recording Gradients of Tem¬ 
perature and Relative Humidity. 

Instruments 

Branch 

MO 4 

JMRP 

No. 17 

May 

1944 

9.014 C 

Notes on Operational Use of Low-Level Meteor¬ 
ological Sounding Equipment. 

K. E. Fitzsimmons 

S. T. Stephenson 

R. W. Bauchman 

Washington 
State Coll. 

Rep. No. 7 

NDRC- 

PDRC-647 

June 15 
1944 

9.015 C 

Microwave Propagation Studies—Detection of 
Troposphere Stratification by Means of Sound 
Echoes—Preliminary Trial—Case 37003. 

H. B. Coxhead 

F. H. Willis 

BTL 

BTL 

MM-44- 

160-143 

June 21 
1944 

9.016 C 

Operating Instructions for the WSC Low-Level 
Atmospheric Sounding Equipment. 

P. A. Anderson 

Washington 
State Coll. 

July 10 
1944 


Rep. No. 8 

NDRC- 

PDRC-647 


9.017 C 

Meteorological Equipment for Short Wave Propa¬ 

W. M. Elsasser 

CUDWR 

August 


gation Studies. 


WPG-3 

1944 

9.018 R 

Wired Sonde Equipment for High Altitude Sound¬ 

L. J. Anderson 

NRSL 

Nov. 17 


ings. (See 9.022.) 


WP-16 

1944 

9.019 C 

Airborne Radiosonde Recorder. 

A. E. Bennett 

Intel. Br. 

Mar. 10 




OCSO USA 
413.6 

1945 

9.020 

KXS Trials—LLANDUDNO June to Sept., 1944. 

F/Lt. J. Cocheme 

JMRP 



Lower Atmosphere Radio-Meteorological Flight 
Technique. 

(RAF) 

No. 55 


9.021 R 

A Note on the Resistance of Electric Hygrometer 

L. J. Anderson 

NRSL 

May 8 


Elements. 

S. T. Stephenson 

AERO-1 

1945 

9.022 R 

improvements in USNRSL Meteorological Sounding 

L. J. Anderson 

NRSL 

July 3 


Equipment. 

S. T. Stephenson 

WP-21 

1945 


(See 9.018.) 

Lt. A. P. D. Stokes 




10.000 RADAR FORECASTING 


10.001 S 

Forecasting of RDF Conditions. 

AORG 

AORG Memo 
No. 103 or 
JMRP No. 2 

May 31 
1943 

10.002 

The Meteorological Aspects of Anomalous Propaga¬ 
tion—Short Wave Radio. 

F/Lt. R. W. 
Hatcher 

JMRP No. 1 

June 

1943 

10.003 S 

Oboe Propagation, Aug.- Oct., 1943. 

H. G. Booker 

TRE T1605 

1943 

10.004 

“Naviprop” Forecasts. 

E. Gold 
(MO) 

SIS 

No. 45 

Nov. 8 
1943 

10.005 S 

Issue of ANOPROP Forecasts—Synoptic Instruction 
Special No. 39. 

MO 

SIS 

No. 39 

Feb. 11 
1944 

10.006 S 

Elements of Radio Meteorological Forecasting 
(Mathematics Group, TRE, Malvern). 

H. G. Booker 

TRE 

T 1621 

Feb. 14 
1944 

10.007 C 

Preliminary Instruction Manual—Weather Fore¬ 

Weather Div. 

Rep. No. 

March 


casting for Radar Operations. 

HQ, AAF 

614 

1944 

10.008 R 

Tropospheric Weather Factors Likely to Affect 

E. Dillon Smith 

U.S. 

July 1 


Superrefraction of VHF-SHF Radio Propagation as 
Applied to the Tropical West Pacific. 

R. D. Fletcher 

Weather 

Bureau 

RP-1 

1944 



296 


GENERAL BIBLIOGRAPHY 


Bib. No. 

Title 

Author or Source 

Number 

Date 

10.009 C 

Preliminary Instruction Manual of Weather Fore¬ 

D. F. Martyn 

CSIR- 

Sept. 4 


casting for Radar Operations in South West Pacific 
Area. 

P. Squires 

RL 

RP 220 

1944 

10.010 C 

Outline of Radio Climatology in India and Vicinity. 

H. G. Booker 

TRE T1727 
or JEIA 6061 
or JMRP No. 25 

Sept. 12 
1944 

10.011 

Notes on TRE Report T.1727-JMRP No. 25 (Radio 

C. S. Durst 

JMRP No. 27 

Nov. 7 


Climatology in India and Vicinity). 

(MO) 

JEIA 10324 

1944 

10.012 

A Note on the Forecasting of AP (Provisional Draft). 

TRE 


Sept. 

1944 

10.013 R 

A Rough Sketch of World Radio Climatology over 
Sea. 

H. G. Booker 

TRE 

T1730 

Oct. 31 
1944 

10.014 C 

American Continents Meteorological Counterparts of 

J. H. Brown 

U.S. 

Nov. 15 


Western Pacific and Indian Ocean Areas as Applied 
to Tropospheric Radio Propagation. 

J. L. Paulhus 

E. Dillon Smith 

Weather 

Bureau 

RP-2 

1944 

10.015 R 

The Possibility of Investigating the Fohn Wind and 

M. A. F. Barnett 

RDL-DSIR-NZ 

Dec. 1 


Sea Breeze Phenomena in N.Z. with A View to Eluci¬ 
dating Certain Problems of Radio-Meteorological 
Forecasting in Other Parts of the World. 

F. E. S. Alexander 

RD 1/471 
or JEIA 

7469 

1944 

10.016 C 

Determination of a Suitable Method of Forecasting 

Lt. J. R. Gerhardt 

AAF Bd. Proj. 

Mar. 10 


Radar Propagation Variations over Water. 

Lt. W. E. Gordon 

#4252R000.77 

1945 

10.017 C 

A Qualitative Outline of the Radio Climatology of 
Australasia. 

H. G. Booker 

TRE T1820 or 
JMRP No. 53 

Apr. 19 
1945 

10.018 C 

determination of the Practicability of Forecasting 

Lt. J. R. Gerhardt 

AAF Bd. Proj. 

June 13 


Meteorological Effects on Radar Propagation. 

Lt. W. E. Gordon 

3767B000.93 

1945 


11.000 ATMOSPHERIC ABSORPTION AND SCATTERING 


11.001 S 

Absorption of 1 Cm. Radiation by Rain. 

M. G. Adam 

R. A. Hull 

C. Hurst 

CVD-CL 

Misc. 3 


11.002 C 

The Absorption of Ultra-Short Wireless Waves in the 
Water Vapour of the Earth’s Atmosphere. 

J. A. Saxton 
(NPL) 

RRB/ 

C 18 

Feb. r 14 

1941) 

11.003 S 

Echo Intensities and Attenuation Due to Clouds, 
Rain, Hail, Sand and Duststorms at Centimeter 
Wavelengths. 

J. W. Ryde 
(GEC) 

GEC 

No. 7831 

Oct. 13 
1941 

11.004 C 

The Atmospheric Absorption of Microwaves. 

J. H. Van Vleck 

RL 43-2 

Apr. 27 
1942 

11.005 S 

The Effect of Rain upon the Propagation of 1 Cm. 
Electro-magnetic Waves—Case 22098. 

S. D. Robertson 
(BTL) 

MM-42- 

160-87 

Aug. 1 
1942 

11.006 S 

The Effect of Rain on the Propagation of Microwaves 
— Case 22098. 

A. P. King 

S. D. Robertson 

MM-42- 

160-93 

Aug. 26 
1942 

11.007 S 

Comparison of Theoretical and Experimental Values 
for the Attenuation of 1 Centimeter Waves in Rain— 
Case 22098. 

S. D. Robertson 
(BTL) 

MM-43- 

160-2 

Jan. 5 
1943 

11.008 S 

An Investigation on the Number and Size Distribu¬ 
tion of Water Particles in Nature. 

Josef Mazur 

F/Lt. Polish 

Air Force 

Met. Res. 

Com. MRP 109 

June 

1943 

11.009 

Report on the Absorption and Refraction of Electro¬ 
magnetic Waves by the Liquid Water, Water Vapour 
and Fog or Rain. 

N. F. Mott 

CRB 

43/2881 

Sept. 2 
1943 

11.010 

Report on the Absorption of Electromagnetic Waves 
in the Wavelength Range 1-100 Cm. by Water in the 
Atmosphere. 

N. F. Mott 

CRB 

43/2882 

Sept. 2 
1943 

11.011 C 

Progress Report on “Verification of Mie Theory- 
Calculations and Measurements of Light Scattering 
by Dielectric Spherical Particles. 

V. K. LaMer 

OSRD 1857 

Div. 10 

NDRC 

Sept. 29 
1943 



GENERAL BIBLIOGRAPHY 


297 


- 


Bib. No. 

Title 

Author or Source 

Number 

Date 


11.000 ATMOSPHERIC ABSORPTION 

AND SCATTERING 

(continued) 


11.012 S 

The Absorption of Centimetric Radiation by Atmos¬ 

J. M. Hough 

USWP 

Apr. 27 


pheric Gases. 

(ADRDE) 

WC 

1944 

11.013 S 

Attenuation Due to Water Drops in the Atmosphere. 

J. M. Hough 

USWP 

Apr. 28 



(ADRDE) 

WC 

1944 

11.014 S 

Propagation of K/2 Band Waves. 

G. E. Mueller 

MM-44- 

July 3 



BTL 

160-150 

1944 

11.015 S 

Interim Report of the USW Panel Working Com¬ 

USWP 

AC 7375/ 

Aug. 14 


mittee. 

WC 

USW 

or JEIA-7607 

1944 


Part I Water in the Atmosphere. 

A. C. Best 


July 18 



MO 


1944 


Part II The Attenuation of Centimetre Waves by 

J. M. Hough 


July 


Atmospheric Gases. 

RRDE 


1944 


Part III Attenuation of Centimetre Waves by Rain, 

J. W. Ryde 

GEC 

Aug. 3 


Hail and Clouds. 

D. Ryde 

GEC 

8516 

1944 


Part IV The Attenuation of Centimetre Waves by 

J. M. Hough 


Aug. 


Rain. 

RRDE 


1944 

11.016 S 

Preliminary Note on Secure Communications on 

TRE 

L/M40/WBL 

Sept. 11 


Millimetre Waves. 


or JEIA 5597 

1944 

11.017 C 

Rotational Line Width in the Absorption Spectrum 

Arthur Adel 

NDRC Div. 14 

Oct. 10 


of Atmospheric Water Vapor and Supplement. 


No. 320 

1944 




Univ. of 

Supp. 




Michigan 

Feb. 1 
1945 

11.018 C 

The Absorption of One-Half Centimeter Electro¬ 

E. R. Beringer 

RL 684 

Jan. 26 


magnetic Waves in Oxygen. 



1945 

11.019 S 

The Effect of Rain on Radar Performance. 

S. C. Hight 

BTL 

Oct. 17 




MM-44-170-50 

1944 

11.020 S 

Measurements of Wave Propagation. 

G. E. Mueller 

BTL 

Feb. 5 




MM-45-160-17 

1945 

11.021 C 

Further Theoretical Investigations on the Atmos¬ 

J. H. Van Vleck 

RL 664 

Mar. 1 


pheric Absorption of Microwaves. 



1945 

11.022 S 

Measurements of the Attenuation of K-Band Waves 

G. T. Rado 

RL 603 

Mar. 7 


by Rain. 



1945 

11.023 S 

Attenuation of Centimetre and Millimetre Waves by 

J. W. Ryde 

GEC 

May 18 


Rain, Hail, Fogs and Clouds. (Draft.) 

D. Ryde 

8670 

1945 

11.024 C 

The Relation Between Absorption and the Frequency 

J. H. Van Vleck 

RL 735 

May 28 


Dependence of Refraction. 



1945 

11.025 S 

Absorption and Scattering of Microwaves by the 

L. Goldstein 

CUDWR 

May 


Atmosphere. 


WPG-11 

1945 

11.026 S 

CVD Progress Report for May, 1945. Part I The 


CVD 

May 


Absorption of K-Band Radiation in Gaseous Am¬ 


CL Prog. 

1945 


monia. 


Rep. 5/45 


11.027 S 

*K-Band Attenuation Due to Rainfall. 

L. J. Anderson 

NRSL 

June 8 



J. P. Day 

C. H. Freres 

J. B. Smyth 

Lt. A. P. D. Stokes 

L. G. Trolese 

WP-20 

1945 


12.000 DIELECTRIC CONSTANT AND LOSS FACTOR 


12.001 R 

A New Method for Measuring Dielectric Constant 

S. Roberts 

MIT 

March 


and Loss in the Range of Centimeter Waves. 

A. von Hippel 

102 

1941 


Wave Guides with Dielectric Sections. 

L. J. Chu 





298 


GENERAL BIBLIOGRAPHY 


Bib. No. 

12.002 C 

12.003 C 

12.004 C 
12.005 C 

12.006 S 
12.007 C 

12.008 S 

12.009 

12.010 C 

12.011 S 

12.012 S 

12.013 S 
12.014 S 
12.015 C 
12.016 C 
12.017 S 
12.018 R 

12.019 C 

12.020 C 

12.021 


Title Author or Source Number Date 

12.000 DIELECTRIC CONSTANT AND LOSS FACTOR (continued) 


The Electrical Properties of Ice. 


The Dielectric Constant and Loss Factor of Water 
Vapour at a Wavelength of 9 Cms. (Frequency— 
3330 Mc/s.) 

The Dielectric Constant of Water Vapour and its 
Effect upon the Propagation of Very Short Waves. 
Progress Report on Ultrahigh Frequency Dielectrics. 

Conductivities of Sea, Tap and Distilled Water at 
X = 10 cm. 

The Measurement of Dielectric Constant and Loss 
with Standing Waves in Coaxial Wave Guides. 

The Dielectric Constant and Absorption Coefficient 
of Water Vapour for Wavelengths of 9 cm. and 3.2 
cm. (Frequencies 3,330 and 9,350 Mc/s.) 

Electrical Measurements on Soil with Alternating 
Currents. 

Auxiliary Equipment for the MIT CO-AX Instru¬ 
ment and Its Use. 


Memorandum on an Electrical Method of Measuring 
the Dielectric Constant of Atmospheric Air, and 
Recording it Continuously. 

The Dielectric Constant and Absorption Coefficient 
of Water Vapour for Radiation of Wavelength 1.6 
cm. (Frequency 18,800 Mc/s.) 

The Dielectric Constant of Water and Ice at Centi¬ 
metre Wavelengths (Working Committee). 
Preliminary Report on the Dielectric Properties of 
Water in the K-Band. 

Transmission and Reflection of Single Plane Sheets. 
(Radome Bulletin No. 4.) 

Recent Dielectric Constant and Loss Tangent Meas- 
surements (on X-Band). (Radome Bulletin No. 5.) 
Dielectric Properties of Water and Ice at K-Band. 

The Interaction Between Electromagnetic Fields and 
Dielectric Materials. 

The Dielectric Properties of Water at Wavelengths 
from 2 mm. to 10 cm. and over the Temperature 
Range 0° to 40° C. 

The Dielectric Properties of Water in the Tempera¬ 
ture Range 0° C. to 40° C. for Wavelengths of 1.24 
cm. and 1.58 cm. 

j The Anomalous Dispersion of Water at Very High 
Radio Frequencies in the Temperature Range 0° to 
40° C. 


T. A. Taylor 

AC 1516/ 

Dec. 22 

W. Jackson 

RDF 110 

Com. 78 

1941 

J. A. Saxton 

DSIR 

Mar. 31 

(NPL) 

RRB/S.l 

1942 

A. C. Stickland 

DSIR 

May 11 

(NPL) 

RRB/S.2 

1942 

A. von Hippel 

Div. 14 

January 


NDRC 

Rep. No. 121 

1943 

L. B. Turner 

ASE 

April 


M.496 

1943 

A. von Hippel 

Div. 14 

April 

D. G. Jelatis 

NDRC 

1943 

W. B. Westphal 

Rep. No. 142 


J. A. Saxton 

DSIR 

June 14 

(NPL) 

RRB/S.ll 

1943 

R. L. Smith-Rose 

JIEE 

Aug. 


(London) 

75, 221-237 

1943 

A. von Hippel 

Div. 14 

Nov. 

D. G. Jelatis 

NDRC 

1943 

W. B. Westphal 

M. G. Haugen 

R. E. Charles 

Rep. No. 210 


TRE 

TRE 

Jan. 6 


M/Memo 15/ 
PEC or 

JMRP No. 8 

1944 

J. A. Saxton 

DSIR 

Apr. 22 

(NPL) 

RRB/S.17 

1944 

J. M. Hough 

USWP 

Apr. 28 

(ADRDE) 

WC 

1944 

C. H. Collie 

CVD Rep. 

May 


CL Misc. 25 

1944 

R. M. Redheffer 

RL- 

July 12 


483-4 

1944 

E. M. Everhart 

RL- 

July 14 


483-5 

1944 

E. L. Younker 

RL 644 

Dec. 4 
1944 

A. von Hippel 

Div. 14 

Jan. 

R. G. Breckenridge 

NDRC 

Rep. No. 122 

1943 

J. A. Saxton 

DSIR 

Mar. 20 

(NPL) 

RRB/C115 

1945 

J. A. Saxton 

DSIR RRB/ 

Mar. 7 

J. A. Lane 

C.116 or 

1945 

(NPL) 

JEIA 9811 


J. A. Saxton 

DSIR RRB/ 

Apr. 6 

(NLP) 

C.118 or 

JEIA 9812 

1945 



GENERAL BIBLIOGRAPHY 


299 


Bib. No. 

Title 

Author or Source 

Number 

Date 


13.000 REFLECTION 

COEFFICIENT 



13.001 C 

Centimeter Wave Propagation over Sea Within the 

H. Archer-Thomson 

ASE 

January 


Optical Range. 

J. C. Dix 

F. Hoyle 

E. C. S. Megaw 

M. H. L. Pryce 

M398 

1942 

13.002 S 

Preliminary Report on the Reflection of 9 Cm. Radi- 

H. Archer-Thomson 

ASE 

Sept. 


ation at the Surface of the Sea. 

N. Brooke 

T. Gold 

F. Hoyle 

M542 

1943 

13.003 C 

Comment on the Reflection of Microwaves from the 

S. O. Rice 

BTL 

Oct. 13 


Surface of the Ocean—II. 


MM-43- 
210-6 

1943 

13.004 S 

S-Band Measurements of Reflection Coefficients for 

E. M. Sherwood 

5220.129 

Oct. 29 


Various Types of Earth. 

Sperry Gyroscope Co. 


1943 

13.005 C 

Special Report on the Determination of the Coeffi- 

W. S. Ament 

NRL 

Nov. 10 


cient of Reflection of Radio Waves at the Ground by 


RA 3A 

1943 


Means of Radar Observations. 


212A 


13.006 

Scattering. 

T. L. Eckersley 

JEIA 3904 

November 



BRL 


1943 

13.007 C 

Preliminary Measurements of 10-Cm. Reflection Co- 

P. J. Rubenstein 

RL- 

Dec. 11 


efficients of Land and Sea at Small Grazing Angles. 

W. T. Fishback 

478 

1943 

13.008 C 

Further Measurements of 3 and 10-Cm. Reflection 

W. T. Fishback 

RL- 

May 17 


Coefficients of Sea Water at Small Grazing Angles. 

P. J. Rubenstein 

568 

1944 

13.009 C 

Microwave Propagation Studies—The Reflection of 

F. H. Willis 

BTL 

July 3 


Sound Signals in the Atmosphere—Case 37003—File 


MM-44- 

1944 


36691-1. 


160-156 • 


13.010 C 

Interim Report on Experiments on Ground Reflec¬ 

L. H. Ford 

DSIR 

July 7 


tion at a Wavelength of 9 cms. 


RRB/C101 
or JEIA 4899 

1944 

13.011 C 

An Experimental Investigation of the Reflection and 

L. H. Ford 

DSIR 

Oct. 27 


Absorption of Radiation of 9 cm. Wavelength. 

R. Oliver 

RRB/C.107 

1944 

13.012 R 

The Measurement of High Reflections at Low Power 

R. M. Redheffer 

RL- 

Nov. 20 


(Radome Bulletin No. 7.) 


483-7 

1944 

13.013 C 

Ground Reflection Coefficient Experiments on X- 

W. M. Sharpless 

BTL 

Dec. 15 


Band. (Case 20564.) 

BTL 

MM-44- 

160-250 

1944 

13.014 C 

The Reflection Coefficient of a Linearly Graded 

BRL 

BRL 

Dec. 


Layer. 


TR 492 

1942 

13.015 C 

Reflection and Scattering. 

T. L. Eckersley 

BRL 

Jan. 




TR 506 

1945 

13.016 S 

Reflection from an Inversion. 

L. E. Beglian 

AC 8210/ 

May 24 



F. J. Northover 

USW 140 
or JEIA 9997 

1945 


14.000 HORIZONTAL AND VERTICAL POLARIZATION 


14.001 

Notes on the Comparison of Vertical and Horizontal 

G. Millington 

BRL 

January 


Polarization in Ground Wave Propagation. 


TR/442 

1940 

14.002 C 

Horizontal and Vertical Polarization. 

T. L. Eckersley 

BRL 

July 




TR/441 

1942 

14.003 S 

The Investigation of Horizontally and Vertically 

T. L. Eckersley 

BRL 

Sept. 


Polarized Direction Finding on Frequencies of the 
Order of 20 to 70 Megacycles per Second. 


TR/451 

1942 

14.004 S 

Polarization Effects and Aerial System Geometry at 

E. C. S. Megaw 

GEC 

Nov. 26 


Centimeter Wavelengths. 

H. Archer-Thomson 
E. M. Hickin 

No. 8101 

1942 



300 


GENERAL BIBLIOGRAPHY 


Bib. No. 

Title 

Author or Source 

Number 

Date 

14.005 S 

Change of Polarization as a Means of Gap Filling. 

R. A. Hutner 

RL- 

Dec. 28 



F. Parker 

B. Howard 

J. Gill 

C-7 

1942 

14.006 S 

Photographic Polarization Tests. 

G. A. Garrett 

RL- 

May 7 


% 

K. L. Mealey 

93-3 

1943 

14.007 R 

Vertical Polarization vs Horizontal Polarization 

R. C. Loring 

CESL 

Oct. 22 


(Tentative Report). 


No. T-l 

1943 

14.008 S 

The Depolarization of Microwaves. 

M. Kessler 

RL 458 

Nov. 1 



C. E. Mandeville 

E. L. Hudspeth 


1943 

14.009 S 

Polarization Studies at S and X Frequencies. 

O. J. Baltzer 

RL 536 

Mar. 14 



W. M. Fairbank 

J. D. Fairbank 


1944 

14.010 S 

Alexandria Palace Tests. 

T. L. Eckersley 

BRL 

October 




TR/498 

1944 


15.000 EFFECT OF HILLS, TREES, OBSTACLES, 

ETC. 


15.001 C 

Screening by Hills. 

H. G. Booker 

TRE 

May 




T1015 

1941 

15.002 

Diffraction Round a Sphere or Cylinder. 

BRL 

TR/433 

March 

1942 

15.003 C 

Centimeter Wave Transmission Measurements from 

H. Archer-Thomson 

GEC 

July 28 


an Ur^an Site. 

E. M. Hickin 

E. C. S. Megaw 

No. 8034 

1942 

15.004 C 

Report on an Investigation of the Propagation of 

NPL 

NPL 

June 2 


Centimeter Waves over Ridges and Through Trees. 


AC 4345/ 

Com. 181 

1943 

15.005 S 

A Note on the Propagation of K Band Waves 

S. D. Robertson 

BTL 

Aug. 13 


Through Trees. Case 22098. 


MM-43- 
160-129 

1943 

15.006 S 

Report on Further Experiments on the Propagation 

NPL 

NPL 

Sept. 6 


of Centimeter Waves Through Trees in Leaf and over 


AC 5059/ 

1943 


Level Ground. 


Com. 197 


15.007 S 

Centimeter Wave Propagation. Notes on the Effect 

R. E. Jennings 

ASE 

Oct. 


of Obstruction by a Single Tree. 

E. C. S. Megaw 

H. Archer-Thomson 
E. M. Hickin 

M.565 

1943 

15.008 S 

An Experimental Investigation on the Propagation of 

J. S. McPetrie 

DSIR 

Oct. 1 


Radio Waves over Bare Ridges in the Wavelength 

L. H. Ford 

RRB/ 

1943 


Range 10 Centimetres to 10 Metres (Frequencies 30 
to 3000 Mc/s.). 

NPL 

S.12 


15.009 S 

Some Observed Effects of Trees upon Microwave 

A. C. Peterson 

BTL 

9/17/43 


Propagation—Case 37003—File 36691-1. 


MM-43- 

Revised 




160-150 

10/15/43 

15.010 R 

Effect of Hills and Trees as Obstructions to Radio 

Jansky and 

Cont. OEMsr- 

Nov. 


Propagation. 

Bailey 

1010: OSRD 
Rep. 3070 

1943 

15.011 C 

On Light Scattering by Spheres I. 

L. Brillouin 

AMG-C 

December 




No. 100 

1943 


NDRC-AMP 
No. 87.1 



GENERAL BIBLIOGRAPHY 


301 


Bib. No. 

Title 

Author or Source 

Number 

Date 


15.000 EFFECT OF HILLS, TREES, 

OBSTACLES, ETC. (continued) 


15.012 

Report on Some Further Experiments on the Effect 

L. H. Ford 

AC 5876/ 

Jan. 20 


of Obstacles on the Propagation of Centimetre Waves. 

A. C. Grace 

Com. 213 

1944 



J. A. Lane 

USW 




(NPL-RD) 

or JEIA 3157 



Addendum to Paper dated 20th January, 1944 en¬ 

L. H. Ford 

AC 5876a/ 

Jan. 1 


titled, “Report on Some Further Experiments on the 

R. Oliver 

Com. 213a 

1945 


Effect of Obstacles on the Propagation of Centimetre 

(NPL-RD) 

USWa 



Waves.” 


or JEIA 7911 


15.013 C 

On Light Scattering by Spheres II. 

L. Brillouin 

AMG-C No. 

April 




132 NDRC-AMP 
No. 87.2 

1944 

15.014 C 

The Propagation of Ultra Short Waves Round Hills 

T. L. Eckersley 

BRL TR.479 

May 


and Other Obstacles. 


or JEIA-5674 

1944 

15.015 R 

Scattering of Radio Raves by Metal Wires and 

F. Horner 

DSIR RRB/ 

Jan. 1 


Sheets. 


C.110 or JEIA 
7793 

1945 

15.016 R 

Some Experiments on the Propagation over Land of 

L. H. Ford 

DSIR RRB/ 

Feb. 15 


Radiation of 9.2 cm. Wavelength. 

NPL 

C.113 

1945 

15.017 C 

A Method of Calculating the Polar Diagram of a 

N. Corcoran 

RRDE 

Mar. 21 


Radio Equipment Standing on Flat Ground Looking 

J. M. Hough 

Res. Rep. No. 

1945 


over a Screen. 


280 or JEIA- 
9113 


15.018 C 

A Preliminary Study of Ground Reflection and Dif¬ 

J. S. Hey 

AORG 

June 28 


fraction Effects with Centimetric Radar Equipment. 

F. Jackson, Capt. 

S. J. Parsons, Maj. 

No. 274 

1945 


16.000 TRANSMISSION OVER PART LAND-PART SEA 


16.001 C 

Diffraction at Coast Line: Sloping Site. 

H. G. Booker 

TRE 

Rep. No. 10 

May 1 

1941 

16.002 

Mixed Land and Sea Transmissions. 

T. L. Eckersley 

BRL 

E.16 

October 

1941 

16.003 S 

Diffraction at Coast Line: Further Numerical Ex¬ 
amples. 

H. G. Booker 

TRE 

Rep. M/35 

Feb. 5 
1942 

16.004 C 

Coastal Refraction. 

BRL 

BRL 

TR/436 

May 

1942 

16.005 C 

Propagation of Wireless Waves over Ground of Vary¬ 
ing Earth Constants (Part Land and Part Sea). 

G. Millington 

BRL 

Marconi 

TR/440 

July 

1942 

16.006 

Transmission over Ground of Varying Earth Con¬ 
stants. 

BRL 

BRL 

TR/473 

July 

1943 

16.007 C 

Diffraction at Coast Line. (Appendix to Report on 
Siting of RDF Stations). 

H. G. Booker 

TRE 

Rep. No. 6 

Jan. 27 
1944 

16.008 C 

Siting and Coverage of Ground Radars. 

E. J. Emmerling, 
Capt., Signal Corps 

CUDWR 

WPG-10 

May 

1945 


17.000 TARGETS AND ECHOES 


17.001 C 

Scattering and Spurious Echoes. 

T. L. Eckersley 

BRL 

TR 437 

April 

1942 

17.002 C 

Reflection of 10 Cm. Radiation by Model Aircraft. 

A. F. Phillips 

ADRDE 
Christchurch. 
Rep. No. 174 

Sept. 8 
1942 

17.CC3 S 

Elementary Survey of Scattering and Echoing by 
Elevated Targets. 

H. G. Booker 

TRE 

M/48/HGB 

Dec. 

1942 

17.004 S 

The Resolution of Composite Echoes with Centi¬ 
meter Wave RDF. 

Maj. J. R. Benson 
Capt. J. A. Ramsay 
P. B. Blow (CAEE) 

CAEE 

4070/ 

C/104 

Feb. 10 
1943 



302 


GENERAL BIBLIOGRAPHY 


Bib. No. 

Title 

Author or Source 

Number 

Date 


17.000 TARGETS AND ECHOES (continued) 



17.005 C 

Microwave Radar Reflection. 

J. F. Carlson 

RL- 

Feb. 20 



S. A. Goudsmit 

43-23 

1943 

17.006 C 

Reflection of Radar Waves from Targets of Simple 

L. J. Anderson 

NRSL 

Feb. 24 


Geometric Form. 

J. B. Smyth 

F. R. Abbott 

WP-3 

1943 

17.007 S 

Radar Echoes from Periscopes. 

J. E. Freehafer 

RL- 

Mar. 1 




42-1 

1943 

17.008 S 

Possible Measurement of Radar Echoes by Use of 

S. A. Goudsmit 

RL- 

Mar. 4 


Model Targets. 

P. R. Weiss 

43-24 

1943 

17.009 S 

Radar Echoes from Atmospheric Phenomena. 

A. E. Bent 

RL- 

Mar. 13 




42-2 

1943 

17.010 S 

Echoes Produced by Perfectly Conducting Objects of 

R. E. B. Makinson 

DSIR 

Mar. 25 


Certain Simple Shapes in Free Space. 


RL 173 

1943 

17.011 S 

Gratings and Screens as Microwave Reflectors. 

RL 

RL- 

Apr. 1 




54-20 

1943 

17.012 S 

Optimum Wavelength for Long Range CW Radar 

W. W. Hansen 

Sperry Gyroscope 

May 1 


Systems. 


Co., Inc. 

Rep. No. 5220- 
126 

1943 

17.013 S 

Report on an Investigation into the Nature of Sea 

TRE 

TRE 

May 12 


Echoes. 


T.1497 

1943 

17.014 S 

The Application of Corner Reflectors to Radar 

R. D. O’Neil 

RL- 

May 14 


(Theoretical). 

F. S. Holt 

P. D. Crout 

43-31 

1943 

17.015 S 

The Application of Corner Reflectors to Radar 

R. D. O’Neil 

RL- 

July 1 


(Experimental). 


55-4 

1943 

17.016 C 

Measurement of the “Effective Echoing Areas” of 

R. Bateman 

OCSO 

July 2 


Various Aircraft. 


ORG-P-8-1 

1943 

17.017 S 

Overwater Observations at X and S Frequencies on 

O. J. Baltzer 

RL- 

July 26 


Surface Targets. 

V. A. Counter 

W. M. Fairbank 

401 

1943 


• 

W. O. Gordy 

E. L. Hudspeth 



17.018 C 

Towed Radar Targets. 

G. A. Armstrong 

ADRDE 

Aug. 6 



G. H. Beeching 

Res. Rep. 

No. 212 

1943 

17.019 C 

Corner Reflector Tests at Langley Field. 

C. M. Gilbert 

RL 402 

Aug. 6 
1943 

17.020 S 

Properties of Corner Reflectors—Case 22098. 

S. D. Robertson 

BTL 

Aug. 12 




MM-43- 

160-130 

1943 

17.021 S 

Use of Corner Reflectors as IFF on Ships. 

Australian ORS 

Oper. Res. 

Aug. 30 



& CSIR-RL 

Rep. No. 24 

1943 

17.022 C 

An Investigation into the Nature of Sea Echoes. 

A.C.Cossor, Ltd. 

MR 109 or 

Sept. 8 



Research Dept. 

Myra Works 

London E10 

JEIA 1221 

1943 

17.023 S 

Bearing Markers for CA No. 1 Sets Provisional In¬ 

J. A. Ramsay 

CAEE 70/ 

Sept. 24 


struction. 


C/157 or 

JEIA 2771 

1943 

17.024 S 

Probability of Detection of Aircraft by RDF. 

T. M. Cherry 

CSIR-RL 

Sept. 30 


• 


MUM.2 or 

JEIA 3954 

1943 

17.025 S 

The Scattering of Radiation from Rectangular Planes, 

Moore School of 

Contract 

Oct. 12 


Half-Cylinders, Hemispheres, and Airplanes. 

Engineering 

W-2279 

1943 



U. of Pa. 

sc-551 

Item 3 




GENERAL BIBLIOGRAPHY 


303 


Bib. No. 

Title 

Author or Source 

Number 


17.000 TARGETS AND ECHOES ( continued) 


17.026 R 

The Theory of Random Processes. 

G. E. Uhlenbeck 

RL 454 

17.027 C 

On the Appearance of the A-Scope when the Pulse 

A. J. F. Siegert 

RL- 


Travels Through a Homogeneous Distribution of 
Scatterers. 


466 

17.028 C 

On the Fluctuations in Signals Returned by Many 

A. J. F. Siegert 

RL- 


Independently Moving Scatterers. 


465 

17.029 S 

The Use of Permanent Echo Amplitudes for Monitor¬ 

F. J. Kerr 

CSIR-RL 


ing S Band Radar Equipment. 

J. F. McConnell 

#RP 177/2 

17.030 C 

The Range Calculator. 

S. J. Mason 

RL- 




497 

17.031 S 

The Performance of 10 Cm. Radar on Surface Craft. 

B. F. Schonland 

AORG 

Rep. No. 155 

17.032 S 

Special Report on Radar Cross Section of Ship Tar¬ 

M. Katzin 

NRL RA 


gets. 


3A 213A 

17.033 S 

Observations of Life Rafts Equipped with Corner 

E. L. Hudspeth 

RL 533 


Reflectors. 

J. P. Nash 


17.034 S 

Radar Cross Section of Ship Targets, II. 

W. S. Ament 

NRL 



M. Katzin 

Rep. No. 



F. C. MacDonald 

R-2232 

17.035 S 

Optical Theory of the Corner Reflector. 

R. C. Spencer 

RL- 




433 

17.036 S 

Observations on Signal Stability at S and X Fre¬ 

O. J. Baltzer 

RL- 


quencies. 

W. M. Fairbank 

J. D. Fairbank 

537 

17.037 C 

Interim Report on the Recognition of Radar Echoes. 

F. E. S. Alexander 

RDL-DSIR 
NZ RD 1/353 
or JEIA 3401 

17.038 S 

Screened and Unscreened Radar Coverage for Surface 

W. Walkinshaw 

TRE 


Targets. 

J. E. Curran 

T.1666 

17.039 S 

The Performance of Naval Radar Systems Against 

F. Hoyle 

JEIA 


Aircraft. 

ASE 

3902 

17.040 S 

Preliminary Report on the Fluctuations of Radar 

H. Goldstein 

RL- 


Signals. 

P. D. Bales 

569 

17.041 S 

Radar Ranging on Land Targets. 

TRE 

TRE 

Memo No. 


* 


101/G 36/ 
ALH 

17.042 R 

The Radar Echoing Power of Conducting Spheres. 

T. Pearcey 

ADRDE 



J. M. C. Scott 

CR 228 

17.043 S 

Use of Corner Reflectors in Beaconry. 

F. J. Kerr 

CSIR-RL 

No. RP.200 
or JEIA 5180 

17.044 C 

Calibration and Standardization of Land Based 

F. R. Abbott 

NRSL 


Radars by the Use of Small Plane Targets. 


WP-12 

17.045 S 

Test of the Pre-Production Model Corner Reflector 


Intel. Br. 


Final Report Project No. E-44-37 AAF Board Project 


OCSO 


No. (M-3) 69, Eglin Field, Florida. 


USA 

413.44/R387.1 

17.046 S 

Radar Cross Section of Ship Targets, III. 

W. S. Ament 

NRL 



M. Katzin 

Rep. No. 



F. C. MacDonald 

R-2295 

17.047 S 

Notes on Echoes and Atmospherics From Lightning 

J. L. Pawsey 

CSIR-RL 


Flashes on P-Band. 


No. RP 

49.2 or 

JEIA 5177 

17.048 S 

Theory of Ship Echoes as Applied to Naval RCM 

T. S. Kuhn 

RRL 


Operations. 

P. J. Sutro 

411-93 


Date 


Oct. 15 
1943 
Nov. 9 
1943 

Nov. 12 
1943 
Dec. 7 
1943 
Dec. 20 

1943 
Jan. 3 

1944 
Jan. 24 
1944 
Feb. 15 
1944 
Feb. 18 
1944 

Mar. 2 
1944 
Mar. 14 
1944 

Mar. 20 
1944 

March 
1944 
Apr. 3 
1944 
May 16 
1944 
May 18 
1944 


May 24 
1944 
June 8 
1944 

June 10 
1944 
June 17 
1944 


June 27 
1944 

July 11 
1944 


July 14 
1944 



304 


GENERAL BIBLIOGRAPHY 


Bib. No. 

Title Author or Source 

17.000 TARGETS AND ECHOES (continued) 

Number 

Date 

17.049 S 

Radar Echoes from the Nearby Atmosphere. Case 
No. 37003-4. 

M. W. Baldwin, Jr. 

BTL 

MM-44- 

150-2 

July 18 
1944 

17.050 S 

Radar Cross Section of Ship Targets IV. 

W. S. Ament 

M. Katzin 

F. C. MacDonald 

NRL Rep. 

No. R-2332 

July 21 
1944 

17.051 S 

Radar Echoes from the Nearby Atmosphere—Second 
Report. Case No. 37003-4. 

M. W. Baldwin, Jr. 

BTL 

MM-44- 

150-3 

July 31 
1944 

17.052 C 

Reflecting Properties of Metal Gratings. 

J. S. Gooden 

CSIR- 
RL No. 

RP 215 

July 31 
1944 

17.053 S 

Theory of the Performance of Radar on Ship Targets 
(ADRDE & CAEE Joint Report). 

M. V. Wilkes 
(ADRDE) 

J. A. Ramsay 

P. B. Blow 
(CAEE) 

ADRDE Ref. 
R04/2/CR252 
or CAEE Ref. 
69/C/149 

July 

1944 

17.054 C 

Corner Reflectors for Life Rafts. 

E. L. Hudspeth 

J. P. Nash 

RL- 

608 

Aug. 1 
1944 

17.055 C 

The Characteristics of S-Band Aircraft Echoes with 
Particular Reference to Radar AA No. 3 MK II. 

G. H. Beeching 

N. Corcoran 

ADRDE 

Res. Rep. 

No. 253 

Aug. 4 
1944 

17.056 S 

Radar Echoes from the Nearby Atmosphere—Third 
Report. Case No. 37003-4. 

M. W. Baldwin, Jr. 

BTL 

MM-44- 

150-4 

Aug. 11 
1944 

17.057 C 

17.058 C 

Considerations Concerning Radar Coverage Dia¬ 
grams. 

RDF Echoes to be Expected from Objects of Various 
Shapes. 

J. L. Pawsey 

Min. of Supply 

DSR 

CSIR 

RL RP-217 

Extra Mural 

Res. F.72/80 

Rep. No. 26 

Aug. 14 
1944 

17.060 S 

Radar Echoes from Shell Bursts at 4 Meters and 50 
cms. Wavelengths. 

S. M. Taylor 

F. E. W. Bugler 

RRDE 

Res. Rep. 

No. 260 

Oct. 9 
1944 

17.061 S 

Summer Storm Echoes on Radar MEW 

J. S. Marshall 

R. C. Langille 

W. J. Palmer 

Capt. R. A. Rodgers 
Capt. G. P. Adamson 
Lt. F. F. Knowles 

CAORG 

Rep. No. 18 

Nov. 27 
1944 

17.062 S 

The Cancellation of Permanent Echoes by the Use of 
Coherent Pulses (Interim Report). 

H. Grayson 

RAE 

Tech. Note 

No. RAD 253 

Nov. 

1944 

17.063 C 

The Fading of S-Band Echoes from Ships in the Opti¬ 
cal Zone. 

R. I. B. Cooper 

RRDE 

Res. Rep. 

No. 265 

Dec. 12 
1944 

17.064 S 

Rotating Corner-Reflectors for Ship Identification. 

J. M. Sturtevant 

RL 654 

NDRC Div. 14 
OEMsr-262 

Jan. 1 
1945 

17.065 R 

Reflection from Smooth Curved Surfaces. 

R. C. Spencer 

RL 661 

Jan. 26 
1945 

17.066 S 

Analysis of Over-Water Tracking. 

E. J. Campbell 

RL 695 

Feb. 12 
1945 

17.067 S 

Technical Report on the Maximum Range of Detec¬ 
tion of the German Early Warning Radar Equipment, 
Especially when Viewing Large, Tight Formations of 
Bomber Aircraft. 

Lt. W. E. Bales 

K. A. Norton 

ORS VIII 

Bomber Comm. 
OCSO OAD-13 

Sept. 13 
1943 

17.068 S 

Performance Checks and Estimation of Vessel Size on 
Shore Based 10 cm. Radar Sets. 

D. Lack 

AORG 

JEIA No. 

3124 

Mar. 30 
1944 




GENERAL BIBLIOGRAPHY 


305 


Bib. No. 

Title Author or Source 

17.000 TARGETS AND ECHOES (continued) 

Number 

Date 

17.069 S 

Report of Trials to Determine the Variations of the 
Apparent Reflecting Point of Plain 10 Cm. Waves 
from a Destroyer. 

J. F. Coales 

M. Hopkins 

ASE 

M 627 

July 

1944 

17.070 C 

The Reflection of Electromagnetic Waves by Long 
Wires and Non-Resonant Cylindrical Conductors. 

J. M. C. Scott 

T. Pearcey 

RRDE 

Res. Rep. 

No. 259 or 

JEIA 7286 

Nov. 13 
1944 

17.071 C 

Theory of Radar Return from the Schnorkel. 

P. M. Marcus 

RL 671 

Jan. 15 
1945 

17.072 S 

Sea Returns and the Detection of Schnorkel. 

(See 17.077.) 

G. G. Macfarlane 

TRE 

T 1787 or 

JEIA 8643 

Feb. 13 
1945 

17.073 S 

Interservice KXS Band Radar Trials. Over Water 
Performance Against Surface Targets. 

J. A.Ramsay,Maj .,RA 
(CAEE & RRDE) 

P. B. Blow, WO II 

H. J. Worsdall 
(ASE) 

ASE M 688 
or JEIA 8820 

February 

1945 

17.074 C 

An Observation of Diffuse Cloud-Like Echoes. 

L. J Pawsey 

F. J. Kerr 

CSIR RL 

RP 246 

Mar. 6 
1945 

17.075 C 

The So-Called Standard Target. 

A. H. Brown 

RL S-43 

Mar. 10 
1945 

17.076 S 

Radar Cross Section of Ship Targets V. 

F. C. MacDonald 

NRL 

R-2466 

Mar. 12 
1945 

17.077 S 

Radar Results Against Schnorkels: A Commentary 
on TRE T. 1787, “Sea Returns and the Detection of 
Schnorkel. ,, 

(See 17.072.) 

Coastal Command 

ORS/CC 

Rep. No. 338 
JEIA 9111 

Mar. 16 
1945 

17.078 C 

Radar Echoes from Clouds of Water Droplets. 

F. Hoyle 

AC 7930/ 

USW 128 

Mar. 16 
1945 

17.079 C 

Comments on “Radar Echoes from Water Droplets.” 
(Paper AC 7930) USW 128 

Lt. R. G. Ross 

AC 7931/ 

USW 129 

Mar. 16 
1945 

17.080 S 

Radar Cross Section of Ship Targets VI. 

W. J. Barr 

NRL 

R-2467 

Apr. 10 
1945 

17.081 C 

S-Band Radar Echoes From Snow. 

J. S. Marshall 

R. C. Langille 

W. M. Palmer 
(CAORG) 

L. G. Tibbies 
(Met. Ser.) 

CAORG 

Rep. No. 26 

June 14 
1945 

17.082 S 

Surface Coverage of Some Shipborne Radar Sets on 

S, X, and K Bands. 

J. D. Fairbank 

W. M. Fairbank 

RL 720 

June 15 
1945 

17.083 C 

Echoes from Tropical Rain on X-Band Airborne 
Radar. 

A. E. Bent 

RL 728 

June 15 
1945 

17.084 S 

Analysis of Storm Echoes in Height Using MHF. 

J. S. Marshall 

Lt. Col. L. G. Eon 
(CAORG) 

L. G. Tibbies 
(Met. Ser.) 

CAORG 

Rep. No. 30 

June 25 
1945 

17.085 S 

k Radar Camouflage. 

M. *M. Andrew 

O. J. Baltzer 

E. L. Hudspeth 
(Project Chairman) 

C. E. Mandeville 

RL 766 

July 16 
1945 



306 


GENERAL BIBLIOGRAPHY 


Bib. No. 

Title 

Author or Source 

Number 

Date 


18.000 DOPPLER 

EFFECT 



18.001 S 

Flutter. A Method of Rapidly and Accurately Ob¬ 

Australian 

Australia 



taining the Velocity of A Ship or Aircraft by RDF 

Operational 

No. 296 



Using Doppler’s Principle. 

Research 

Oper. Res. 




Group 

Rep. 21 


18.002 S 

“S” Band Doppler Experiment—Case 20564. 

W. M. Goodall 

BTL 

Oct. 20 



C. F. P. Rose 

MM-43- 

160-173 

1943 

18.003 S 

The Detection of Moving Targets Among Ground 

R. A. McConnell 

. RL 480 

Dec. 14 


Clutter by Coherent Pulse Methods. 



1943 

18.004 S 

The Elimination of Ground Clutter. 

E. C. Pollard 

RL 526 

Mar. 13 
1944 

18.005 C 

Pulse Doppler with Reference to Ground Speed Indi¬ 

D. Sayre 

RL 63- 

Mar. 20 


cation. 


3/20/44 

1944 

18.006 S 

Pulse Doppler for Detection of Moving Ground Tar¬ 

R. F. Thomson 

RL 553 

Apr. 21 


gets. 



1944 

18.007 S 

Anti-Clutter in North America (Report on A Visit to 

W. S. Elliot 

Intel. Br. 

August 


U.S. and Canada). 


GB 413.44/ 

R170 

1944 

18.008 S 

Tests on the Doppler B-scope Presentation of Moving 

A. E. Bailey 

RRDE 

Feb. 12 


Targets. 

W. S. Elliot 

Memo 82 or 

1945 


H. Pursey 

JEIA 8250 



19.000 COMMUNICATION 

(TROPOSPHERIC) 



19.001 

Data on Wave Propagation (10 Kilocycles to 60 

R. S. Baldwin 

NRL 

Aug. 20 


Megacycles). 

L. C. Young 

Rep. No. 

R-1300 

1936 

19.002 S 

Study of Field Strength Records Obtained on the 

R. L. Smith-Rose 

DSIR 

Sept. 1 


Post Office Ultra-Short-Wave Radio Telephone Link 
Between Guernsey and England. (Wavelength 5 m 
and 8 m). 

A. C. Stickland 

RRB/C.39 

1941 

19.003 C 

3000 Megacycle Communication. 

H. H. Beverage 

NDRC- 

Mar. 10 



RCA 

PDRC-90 

1942 

19.004 C 

Microwave Telephone. Part I: Omnidirectional. Part 

H. H. Beverage 

NDRC- 

Mar. 22 


II: Directional. 

RCA 

SC-13 

1943 

19.005 S 

Trials of WS No. X 20. A. 

British 

AC 4139/ 

June 2 



Min. of Supply 

Com. 176 

1943 

19.006 R 

Factors Determining the Range of Radio Communi¬ 

J. W. Herbstreit 

OCSO 

June 3 


cations in the Various Theaters of Operation. 


ORG-P-14-1 

1943 

19.007 C 

Radiotelephone Communication on 3000 Megacycles. 

P. A. Anderson 

Wash. State 

June 12 



K. E. Fitzsimmons 

Coll. Rep. 

1943 



C. L. Barker 

No. 2 




S. T. Stephenson 

NDRC-PDRC 

647 


19.008 S 

An Analysis of the Effect of Frequency on Short Dis¬ 

R. Bateman 

OCSO 

Aug. 18 


tance Radio Communications. 

W. Q. Crichlow 

ORB-P-15-1 

1943 

19.009 C 

Use of the 25 to 50 Mc/s Band for Short Range Wire¬ 

English 

AORG 

Aug. 27 


less Communication. 

AORG 

No. 130 

1943 

19.010 S 

Trials with a 250-Watt Frequency-Modulated VHF 

G. W. Higgins 

SRDE 

Sept. 


Sender Across a Sea Water Path Beyond the Optical 
Range. 

Capt. W. H. Hill 

No. 878 

1943 

19.011 S 

Radio Communication in Jungles. 

A. C. Omberg 

OCSO 

Sept. 1 


4 


ORG-2-1 

1943 

19.012 C 

Measurement of Factors Affecting Jungle Radio 

J. W. Herbstreit 

OCSO 

Nov. 10 


Communication. 

W. Q. Crichlow 

ORB-2-3 

1943 

19.013 R 

Methods for Improving the Effectiveness of Jungle 

War Dept. 

War Dept. 

Jan. 14 


Radio Communication. 


TB Sig 4 

1944 



GENERAL BIBLIOGRAPHY 


307 


Bib. No. Title Author or Source Number 


19.000 COMMUNICATION (TROPOSPHERIC) (continued) 


19.014 R 

Survey of Existing Information and Data on Atmos¬ 

H. A. Thomas 

DSIR 


pheric Noise Level over the Frequency Range 1-30 

R. E. Burgess 

RRB/C.90 


Mc/s. 

NPL 

or JEIA 

2815 

19.015 S 

Proposals for Provision and Application of Propaga¬ 
tion Data for Operational & Field Use with Wireless 
Equipment in the Centimetre Band. 

Lt. E. W. Walker 

SRDE 

No. 908 

19.016 C 

Methods of Reducing Radar Interference to Com¬ 
munication. 

ORB 

OCSO 

ORB-E-27-2 

19.017 C 

The Application of Passive Repeaters to Point to 
Point Communication at YHF and UHF. 

R. Bateman 

OCSO 

ORB-P-20-1 

19.018 R 

Point to Point Communication in VHF Band Via 
Ground Wave Propagation. (Southwest Pacific Area.) 

W. C. Babcock 

JEIA 6768 or 
Intel. Br. 
OCSO 

SWPA 413.44/ 
R423.5 

19.019 R 

Ground Wave Radio Propagation Report. (South¬ 
west Pacific Area.) 

W. C. Babcock 

JEIA 6769 or 
Intel. Br. 
OCSO 

SWPA 413.44/ 
R113 

19.020 S 

Summary of Radio Propagation Problems in South¬ 
west Pacific Area. 

And 

W. C. Babcock 

JEIA 6298 or 
Intel. Br. 

OCSO 

US/413.44/ 

R113 


Point to Point Communication in MF Band Via 
Ground Wave Propagation. 

W. C. Babcock 

JEIA 6770 or 
Intel. Br. 

OCSO 

SWPA 413.44/ 
R423.4 

19.021 C 

Measurements of Factors Affecting Radio Communi¬ 

R. Bateman 

OCSO 


cation & Loran Navigation in SWPA. 

J. W. Herbstreit 

R. B. Zechiel 

ORB-2-4 

19.022 S 

Field Trials of Ultra Short Wave Frequency and 

A. W. Pearson 

POED 


Amplitude Modulated Multichannel Radio Tele- 

W. J. Bray 

Radio Rep. 


phone Systems. J. H. H. Merriman 

R. W. White 

J. G. Hobbs 

C. H. Gibbs 

H. Prain 

20.000 UNDER-WATER SOUND PROPAGATION 

No. 1115 


Included in this Bibliography because of the similarity of problems. 

20.001 R 

Sound Transmission in Sea Water. (A Preliminary 
Report.) 

Woods Hole Oceano¬ 
graphic Institution 
for NDRC 


20.002 C 

Some Characteristics of the Sound Field in the Sea. 

Oceanographic 
Division. U.C. 

NDRC 

C4-sr30-083 

20.003 C 

Theoretical Discussion of Reverberation. 

C. L. Pekeris 
Columbia Univ. 

NDRC 

C4-sr20-097 

20.004 C 

Sound Ranges under the Sea. 

T. H. Osgood 
Columbia Univ. 

NDRC 

C4-sr20-100 

20.005 C 

Reverberation in Echo Ranging, Part I, General 

W. V. Houston 

NDRC 


Principles. 

T. H. Osgood 
Columbia Univ. 

C4-sr20-140 


Date 


Feb. 21 
1944 


Feb.-Mar. 

1944 

Apr. 19 
1944 
Apr. 29 
1944 
July 24 
1944 


Aug. 15 
1944 


Sept. 6 
1944 


Aug. 15 
1944 


Dec. 16 
1944 

Mar. 27 
1944 


Feb. 1 

1941 

Mar. 13 

1942 
May 29 
1942 
June 5 
1942 
July 28 
1942 




308 


GENERAL BIBLIOGRAPHY 


Bib. No. Title Author or Source Number Date 

20.000 UNDER-WATER SOUND PROPAGATION (continued) 


20.006 C 

Attenuation of Underwater Sound. 

F. A. Everest 

H. T. O’Neil 

UCDWR- 

NDRC 

C4-sr30-494 

2/16/42 

Revised 

7/30/42 

20.007 C 

Reverberation Studies at 24 KC. 

Reverberation 
Group, Univ. 
of California 

UCDWR-U7 
NDRC-Sec. 6.1 
sr30-401 

Nov. 23 
1942 

20.008 C 

Transmission of Explosive Impulses in the Sea. 

T. F. Johnston 

R. W. Raitt 

UCDWR-U8 

NDRC 

C4-sr30-403 

Dec. 2 
1942 

20.009 C 

Variation of the Sound Field Near the Surface in 
Deep Water. 

H. T. O’Neil 

T. F. Johnston 

UCDWR-U49 
NDRC-Sec. 6.1 
sr30 

Mar. 16 
1943 

20.010 C 

Reverberation in Echo Ranging, Part II. Reverbera¬ 
tion Found in Practice. 

T. H. Osgood 

CUDWR 
NDRC-Sec. 6.1 
sr20-840 

Apr. 14 
1943 

20.011 C 

Theory of Diffraction of Sound in the Shadow Zone. 

C. L. Pekeris 

CUDWR 
NDRC-Sec. 6.1 
sr20-846 

May 5 
1943 

20.012 C 

Reflection of Sound in the Ocean from Temperature 
Changes. 

R. R. Carhart 

UCDWR-U74 
NDRC-Sec. 6.1- 
sr30-960 

May 17 
1943 

20.013 C 

The Discrimination of Transducers Against Rever¬ 
beration. 

Reverberation 
Group, Univ. 
of California 

UCDWR-U75 
NDRC Sec. 6.1 
sr30-968 

May 31 
1943 

20.014 C 

The Propagation of Sound in Shallow Water. 

G. M. Roe 

Bureau of Ships 

BuShips 

Rep. 65 

June 3 
1943 

20.015 C 

Some General Ideas Concerning the Transmission of 
Sound in the Deep Sea. 

C. Eckart 

UCDWR No. 
M108 NDRC 

Sec. 6.1-sr30 

Sept. 28 
1943 

20.016 C 

Interim Report on the Sound Field of Echo-Ranging 
Gear. 

NRSL& 

U. of Calif. 

UCDWR No. 
U113 NDRC 

Sec. 6.1- 
sr30-1206 

Oct. 1 
1943 

20.017 C 

Conclusions Derived from the Analysis of Trans¬ 
mission Data Obtained During Harbor Surveys (Pre¬ 
liminary Draft, Part I). 

UCDWR 

UCDWR No. U110 Oct. 2 
NDRC 1943 

Sec. 6.1-sr30 

20.018 C 

Lloyd Mirror Effect in a Variable Velocity Medium. 

R. R. Carhart 

U. of Calif. 

UCDWR 

M 140 NDRC 

Sec. 6.1-sr30 

Oct. 23 
1943 

20.019 C 

20.020 C 

A Survey of the Problem of Maximum Echo Ranges 
(Preliminary Draft). 

Use of Submarine Bathythermograph Observations 
(Revision of Rules for Predicting Maximum Sound 
Ranges). 

C. Eckart 

U. of Calif. 

UCDWR-U130 
NDRC Sec. 6.1 
sr30-1315 

NAVSHIPS 

943-F 

Nov. 20 

1943 

1944 

20.021 C 

Maximum Echo Ranges—Their Prediction and Use. 

U: of Calif. 

UCDWR-NDRC 
Sec. 6.1- 
sr30-1460 

January 

1944 

20.022 C 

Sound Transmission Through Destroyer Wakes. 

Listening Section 

UCDWR-M189 
NDRC Sec. 6.1- 
sr30 

Mar. 8 
1944 

20.023 C 

Some Experiments on the Transmission of Con¬ 
tinuous Sound in 100-Fathom to 600-Fathom Water. 

Listening Section 

UCDWR-M193 
NDRC Sec. 6.1- 
sr30 

Mar. 15 
1944 

20.024 C 

Effect of the Thermocline on the Propagation of 
Sound. 

P. S. Epstein 

U. of Calif. 

UCDWR 

Rep. No. 5 

Mar. 19 
1944 




GENERAL BIBLIOGRAPHY 


309 


Bib. No. 

Title 

Author or Source 

Number 

Date 

* 

20.000 UNDER-WATER SOUND PROPAGATION (continued) 


20.025 C 

Prediction of Sound Ranges from Bathythermograph 
Observations. (Rules for Preparing Sonar Messages.) 


NAYSHIPS 

943-C2 

March 

1944 

20.026 C 

Preliminary Report on the Sonic Ray Plotter. 

L. I. Schiff 

U. of P. for 

U. of Calif. 

UCDWR 

M 207 

Apr. 21 
1944 

20.027 C 

Current Methods for Prediction of Maximum Sound 

Sonar Analysis 

CUDWR 

May 1 


Ranges. 

Section 

Tech. Memo 

No. 1 

1944 

20.028 C 

The Attenuation of Sound in the Sea. 

C. Eckart 

U. of Calif. 

UCDWR-U236 
NDRC Sec. 6.1- 
sr30-1532 

July 6 

1944 

20.029 C 

The Sonic Ray Plotter. 

L. I. Schiff 

U. of P. for 

U. of Calif. 

UCDWR-U246 
Sec. 6.1- 
sr30-1741 

Aug. 8 

1944 

20.030 C 

Sound Ranges under the Sea. (Revision of Report 

Sonar Analysis 

CUDWR NDRC 

November 


dated June 5, 1942.) 

Section 

Sec. 6.1-srll- 
31-1880 

1944 

20.031 C 

Prediction of Sonic and Supersonic Listening Ranges. 

Sonar Analysis 
Section 

CUDWR NDRC 
Sec. 6.1- 
srll31-1884 

December 

1944 

20.032 C 

Relation Between Scattering & Absorption of Sound. 

Sonar Analysis 
Section 

CUDWR 

Memo for 

File SAS-8 

Dec. 11 
1944 

20.033 C 

Coherence of CW Reverberations. 

Sonar Analysis 
Section 

CUDWR 

Memo for 

File SAS-11 

Dec. 20 
1944 

20.034 C 

Distribution of Amplitude if Two Rays with Random 

Sonar Analysis 

CUDWR 

Jan. 4 


Phase and Given Amplitude Distributions Interfere. 

Section 

Memo for 

File SAS-13 

1945 

20.035 C 

Fluctuations of Transmitted Sound in the Ocean. 

Sonar Analysis 
Section 

CUDWR 

Tech. Memo 

No. 6 

Jan. 17 
1945 

20.036 C 

Lloyd Mirror Effect in the Presence of a Temperature 

Sonar Analysis 

CUDWR 

Jan. 22 


Gradient. 

Section 

Memo for 

File SAS-17 

1945 

20.037 C 

Change of Average Peak Echo Intensity with Chang¬ 

Sonar Analysis 

CUDWR 

Mar. 22 


ing Ping Length. 

Section 

Memo for 

File SAS-30 

1945 

20.038 C 

The Wave Equation with Gravitational Terms. 

Sonar Analysis 
Section 

CUDWR 

Memo for 

File SAS-37 

June 18 
1945 


a TM 11-486 (Apr. 25, 1945) together with TM 11-487—"Electrical Communication Systems Equipment.” (Oct. 2, 1944) supersedes TM 
11-486 (Feb. 25, 1944). 

b See also 1.012 Part I. 

c See also 1.012 Parts I, VIII, and XIV. 

d See also 1.012 Part IV. 

e See also 1.012 Parts III and IX, 5.049, 15.016, and 17.073. 

*See also 1.012 Part XII and XIII, 6.028, 6.031, and 6.037. 

8See also 1.012 Part VI and 6.035. 

b See also 1.012 Parts V, VII, XII, and XV, 1.014 and 8.028. 

•See also 1.012 Part II, 17.061 and 17.081. 

• See also 13.012. 
k See also 6.035 and 11.003. 







OSRD APPOINTEES 


Committee on Propagation 

Chairman 

Chas. R. Burrows 


H. H. Beverage 
T. J. Carroll 

J. H. Dellinger 

Members 

Martin Katzin 
D. E. Kerr 

J. A. Stratton 

S. S. Attwood 

Consultants 

C. E. Buell 


J. A. Stratton 

Technical Aides 

(Listed in the order they served.) 
A. F. Murray 
S. W. Thomas 
R. J. Hearon 






I 


CONTRACT NUMBERS, CONTRACTORS AND SUBJECT OF CONTRACTS 


Contract Numbers 

Name and Address of 
Contractor 

Subject 

OEMsr-1207 

Columbia University 

New York City, New York 

Correlation, analysis and integration of data on radio and radar 
propagation. 

OEMsr-728 

State College of Washington 
Pullman, Washington 

Develop meteorological equipment and conduct meteorological 
soundings in the Southwest Pacific and correlate it with radio 
propagation data. 

OEMsr-1497 

Humble Oil & Refining Company 
Houston, Texas 

Development and construction of microwave field strength measuring 
sets. 

OEMsr-1496 

University of Texas 

Austin, Texas 

Development of equipment for and making measurements of time 
and space deviations in radio wave propagation. 

OEMsr-1502 

Jam Handy Organization, Inc. 
Detroit, Michigan 

Preparation of a General Outline of Training Material and the 
preparation of manuals, films and other training aids for use in 
instructing technical and other personnel in radio-weather and 
radio propagation. 


311 





SERVICE PROJECTS 


The Committee on Propagation did all of its work under 
Project Control SOS-9, which was originally set up through 
the request of the Combined Chiefs of Staff following recom¬ 
mendations submitted by the Combined Meteorological Com¬ 
mittee: (a) That the Committee on Propagation of the 
National Defense Research Committee be requested to act 
as a coordinating agency for all meteorological information 
associated with short wave propagation; (b) That the Com¬ 
mittee on Propagation be requested to forward periodically 
to the CMC a list of all reports and papers dealing with the 
meteorological aspects on short wave propagation which have 
been received or transmitted by that Committee. 

Later the Combined Meteorological Committee in its 37th 
meeting on Tuesday, February 22, 1944, agreed, that “the 
National Defense Research Committee [NDRC], Committee 
on Propagation, be recognized as the supervising committee 
on all basic research being done in the United States on the 
related problems of radar propagation and weather, in addi¬ 
tion it shall be the recognized channel whereby international 
exchange of papers of the two related sciences will be effected.” 

The Joint Communications Board therefore approved the 
following policy, which was concurred in by NDRC and by 
the Joint Meteorological Committee: 

1. The NDRC Propagation Committee and its associated 
working groups will initiate and exercise technical supervision 
over such tests and investigations as they deem necessary to 
ascertain the nature of the above-mentioned propagation 
anomalies in the VHF, UHF, and SHF bands, to devise the 
most practicable methods to determine the occurrence and 
characteristics of these anomalies from appropriate meteor¬ 
ological forecasts, with a view to improving the interim solu¬ 


tions offered by the Joint Wave Propagation Committee of 
the JCB. 

2. The Army and Navy will furnish by direct coordination 
between them the basic staff guidance for such tests and in¬ 
vestigations. They will accomplish this by determining: 

a. The specific forms in which* basic prediction data 
shall be presented, and 

b. The method of use required for operational forecast 
of propagation anomalies in the VHF, UHF, and SHF 
bands. 

3. When the NDRC requires the cooperation of the oper¬ 
ating units of the Army and Navy in conducting such tests and 
investigations as it deems necessary and this cooperation is 
of such an extent and nature that it cannot be furnished by 
informal coordination, it will be requested through the Joint 
Wave Propagation Committee of the JCB. Such requests will 
be initiated by the NDRC representative on the Wave Propa¬ 
gation Committee and recommended to the Joint Communi¬ 
cations Board by the Joint Wave Propagation Committee for 
consideration. 

4. The Joint Wave Propagation Committee will be respon¬ 
sible for devising and furnishing immediately, interim oper¬ 
ational forecasting guides based upon information already 
available. 

On April 3, 1944, the Coordinator of Research and Develop¬ 
ment requested that the Army Project SOS-9 be made a joint 
Army-Navy project. Project No. AN-16 was assigned to this. 

On May 23, 1944, the Chief Signal Officer requested that 
under Project AN-16 the following work be inaugurated: 

Project AC 230.04 “Wave Propagation Study of Line-of- 
Sight Communication and Navigation.” 


312 



/ 


INDEX 

The subject indexes of all STR volumes are combined in a master indek 
For access to the index volume consult the Army or Navy Agency listed on t 


Absorption of microwaves, 

82-90, 222-224 
atmospheric gases, 89-90 
rain and hail, 85-88 
water drops, 222-224 
Advection, definition, 75-76, 212 
Advective ducts, coastal and maritime 
conditions, 77-78, 213-214 
Airplane radar cross sections, 83-84 
Angle-of-arrival measurements, 73-74 
Antenna patterns for ground radar, 
162-167 

earth curvature effect on lobe 
lengths, 166-167 
factors, 164 

local terrain effects, 164-166 
reflecting screen, 163 
vertical patterns, 162, 164 
Antigua transmission experiments, 

71-73 

Atmospheric refraction 

see Atmospheric stratification and 
refraction; Radar errors due to 
atmospheric refraction 
Atmospheric stratification and 
refraction, 75-76, 198-210 
advection, 75-76 
attenuation, 207 
convection, 76 

duct, superrefraction, 204-207 
frictional turbulence, 76 
measurement of refractive index, 200 
nocturnal cooling, 75-76 
operational applications, 208-210 
origin of refractive index variations, 
198-200 

rays in stratified atmosphere, 

202-204 

reflection from elevated layer, 208 
subsidence, 76 
temperature inversions, 76 
types of modified index curves, 202 
wave picture of guided propagation, 
207-208 

Attenuation diagrams for surface ducts, 
240 

Bending of radio waves, 178-180 
Bilinear M curve, first mode, 228-232 
completely trapped modes, 232 
depth loss, 231 
leaky modes, 232 

surface barrier strength increase, 231 
undiscovered solution, 231-232 
Bilinear M curve, second and higher 
modes, 234-236 


British transmission experiments, 

58-60 

Irish Sea experiment, 58-59 
overland path, 59-60 

Calculations for second and higher 
modes of bilinear model, 234-236 
Calibration and testing of ground 
radars, 174-177 

Canadian transmission experiments, 67 
Captive balloons and kites, 52 
Characteristic values for bilinear M 
curve 

first mode, 228-232 
second and higher modes, 234-236 
Chronological record of Committee 
on Propagation activities, 13-24 
1943; 13-14 
1944; 14-20 
1945; 20-24 

Anderson’s southwest Pacific 
Theatre work, 17-21 
program adopted, 15-16 
specific experiments outlined, 14-15 
Circuit reliability, 222 
Cloud echoes in radar, 184-185 
Coastal and maritime conditions, 
meteorology, 77-78 
advection, 77, 213-214 
duct formation, 77-78 
Contracts and projects, 11-12 
Columbia University, 11 
Combined Chiefs of Staff request, 11 
Humble Oil Company of Texas, 12 
Jam Handy Organization of Detroit, 
12 

State College of Washington, 11 
University of Texas, 12 
Convection, 212 

Convergence effects in reflections from 
tropospheric layers, 258-259 
conclusions, 259 
convergence factor, 258-259 
roughness effect, 259 
Cornu’s spiral, 127-128, 131-132 
Coverage diagram, 190-193 
complex cases, 193 
definition, 190 

magnitude of field intensity, 190-191 
nomographic solutions, 95-105 
simple cases, 191-193 

Diffraction of radio waves, 120-134 
by terrain, 37-38 
Cornu’s spiral, 127-128, 131-132 
Fresnel integrals, 125-127 


printed in a separate volume, 
le reverse of the half-title page. 

Fresnel zones, 121-123 
limitations of Fresnel theory, 
133-134 

location of maxima and minima, 
129-131 

multiple slits and obstacles, 133 
narrow obstacle, 132-133 
obstacles, 124-125 
over hills, 110-112 
Rayleigh criterion, 123-124 
rectangular slit, 131-132 
reflection from rough surfaces, 
123-124 

shoreline, 158, 162 
straight edge diffraction, 128-129 
wave propagation, 121 
Diffraction zone, nonstandard 
propagation 

see Nonstandard propagation in 
diffraction zone 

Divergence factor for reflected wave, 

170 

Ducts 

characteristics in nonstandard 
propagation, 46-47 
fades, 220 
formation, 79 
over open ocean, 214-215 
superrefraction, 204-207 
surface, attenuation diagram, 240 
Dynamic effects in lower atmosphere 
fronts, 79 

high pressure area, 79 
low pressure area, 78-79 
subsidence, 78-79 

Early warning heightfinding radar, 
106-109 

Earth curvature effect on radar 

antenna lobe lengths, 166-167 
Electromagnetic field, 38-41 
attenuation factor, 41 
field strength distribution, 38-39 
modes, 39-41 

Equipment tests for ground radar, 
174-175 

Errors in radar due to atmospheric 
refraction 

see Radar errors due to atmospheric 
refraction 

Fading on different wavelengths, 
221-222 

Fixed echo control, shielding, 137 
Flat earth lobe angle calculations, 
147-149 


313 


314 


INDEX 


Fog 

effect on refractive index, 77, 216 
effect on signal strength, 221 
Forecasting and meteorology 
see Meteorology and forecasting 
Formula for lobe, radar, 171-174 
Formula for lobe angle, radar, 152-155 
Formula for reflection area, 160-162 
Fresnel formulas for reflection 
coefficient, 32-33 
Fresnel integrals for diffraction 
phenomena, 125-127 
Fresnel theory, limitations for 

diffraction problems, 133-134 
Fresnel zones, 121-123, 158-162 
Fresnel-Kirchhoff diffraction theory, 
37 

Frictional turbulence, 212-213 

Gaussian distribution, 259 
Graphical method for determination of 
standard coverage charts, 93-94 
Ground and sea reflection, 28 
Ground radar, antenna patterns 
earth curvature effect on lobe 
lengths, 166-167 
factors, 164 

local terrain effects, 164-166 
reflecting screens, 163 
vertical patterns, 162, 164 
Ground radar, equipment, 106-109 
conclusions, 109 
derivation of formulas, 109 
early warning heightfinding radar, 
106-109 

gunlaying (antiaircraft) radar, 
106-107, 109 

surface surveillance radar, 108 
tests, 174-175 

Ground radar, siting and coverage, 
113-177 

calculation of vertical coverage, 
145-174 

calibration and testing, 174-177 
diffraction of radio waves, 120-134 
permanent echoes, 134-145 
radar systems, 113-115 
signal measurements, 175-176 
topography of siting, 115-120 
Ground radar, test data analysis, 
176-177 

calibrated receiver method, 177 
maximum free space range, 176-177 
signal-to-noise graph, 176 
Ground radar, types, 113 
Ground reflection, 190-193 
Ground roughness estimation, 36-37 
Guided propagation, 179-182 
see also Superrefraction 
coverage, 181-182 
critical angle, 181 


definition, 190 
duct, 181-182 
equipment faults, 182 
in nonhomogeneous atmosphere, 
244-246 

occurrence causes, 185 
wave picture, 207-208 

Gunlaying (antiaircraft) radar, 

106-107, 109 

Hankel functions in propagation 
equation solution, 237-239 

Heightfinding radar, early warning, 
106-108 

Height-gain functions, 255 

Historical background for nonstandard 
propagation, 42 

History of Committee on Propagation, 
5-27 

chronological record of activities, 
13-24 

contracts and projects, 11-12 
critique, 26 

investigating bodies, 10 
liaison channels, 8 
objectives, 9-10 
organization, 6-7 
origin, 5-8 

research recommendations, 26-27 
results, 25-26 

Humidity and temperature in 

meteorological measurements, 

50 

Huyghens’ principle, wave 
propagation, 121 

Incipient leakage in surface duct, 
233-234 

attenuation constant, 233 
conclusion, 234 

Freehafer and Furry formula, 233 

Irish Sea transmission experiment, 
58-59 

Leaky waveguide theory, 48 

Lobe angle calculations, 147-158 
computing methods, 155 
correction for standard earth 
curvature, 149-152 
diagrams of medium height sites, 
158 

flat earth, 147-149 
formula, 152-155 
general lobe formula, 171-174 
lobe lengths, 166-167, 170 
low site lobes, 155-156 
reflection area, general formula, 
160-162 

sea reflection with diffuse land 
reflection, 158-159 
shoreline diffraction, 158, 162 


Lobes for medium height radar, 170 

Local terrain effects on antenna 
pattern, 164-166 
cliff edge diffraction, 166 
land reflection and diffraction, 166 
limited reflecting area, 165 

M curves, 43, 55-57 

Meteorological factors in radar 
coverage, 182-184 
air turbulence, 184 
measurements, 184 
occurrence frequency of guided 
propagation, 184 
over land, 183-184 
over sea, 183 
refraction causes, 182-183 
subsidence, 184 

temperature inversion, 182-184 
trapping, 182-184 

Meteorological measurements, 50-57 
anemometers, 55-56 
M curves, 55-57 
noncaptive radiosonde, 52-55 
psychrometer, 52-55 
refractive index measurements, 52 
temperature and humidity elements, 
50 

wired sonde, 51 

Meteorology and forecasting, 75-81 
atmospheric stratification, 75-76 
coastal and martime conditions, 
77-78 

conditions over land, 76-77 
dynamic effects, 78-79 
fog, 77 

radar forecasting, 80-81 
radio forecasting, 75 
world survey, 79-80 

Microwave permanent echoes, 144-145 

Microwaves, scattering and absorption 
see Scattering and absorption of 
microwaves 

Moisture gradients, 210-212 

Nocturnal cooling, 75-77, 212, 215-216 

Nomographic solutions for coverage 
diagrams, 95-105 

Nonoptical radio transmission path, 
221-222 

Nonstandard propagation, 42-49 

continuously varying modified index 
curve, 247-248 
duct characteristics, 46-47 
historical background, 42 
in ocean surface duct, 247 
operational applications. 208-210 
perturbation theory for exponential 
M curve, 249-255 
ray tracing, 44-45 
reflection from elevated layers, 49 





INDEX 


315 


refractive index, 42-44 
symbols, 255 

waveguide theory survey, 47-48 
Nonstandard propagation, operational 
applications, 208-210 
ground clutter interference, 208 
radio countermeasures, 210 
superrefraction, 208-210 
VHF navigational aids, 209-210 
Nonstandard propagation in diffraction 
zone, 226-227 
complex arguments, 227 
Eckersley modes, 226 
Gamow modes, 226 
horizontal attenuation of various 
modes, 226 

numerical integration method, 
226-227 

phase integral methods, 227 

Oceanic surface duct, propagation in, 
247 

Optical properties of earth surface and 
atmosphere, 32-38 
diffraction by terrain, 37-38 
electromagnetic properties of ground, 
32-33 

Fresnel formulas, 32-33 
Fresnel-Kirchhoff diffraction theory, 
37 

horizontal polarization, 32-34 
Rayleigh criterion for roughness of 
ground, 36-37 
reflection coefficients, 32-34 
roughness of ground, 36-37 
Snell’s law, 36 
standard refraction, 34-36 
vertical polarization, 32-33 
Organization of propagation research 
program 

initial committee membership, 7 
liaison channels, 8 
program plan, 6-7 
Overland path transmission 
experiment, 59-60 

Permanent echo diagrams, 134-135 
plotting data, 135 
typical preparation, 134-135 
uses, 134 

Permanent echo prediction, 137-144 
methods of determination, 137 
profile method, 137-144 
radar planning device technique, 
137-138 

supersonic method, 138 
Permanent echoes in radar siting 
diagrams, 134-135 
microwaves, 144-145 
prediction of permanent echoes, 
137-144 


reasons for variations, 135-136 
shielding, 137 
testing uses, 135-137 
troublesome factors, 134 
Perturbation theory for M curve in 
nonstandard propagation, 
249-255 
abstract, 249 

application to general class of 
M anomalies, 254 
computational program for 

exponential model, 254-255 
evaluation of indefinite integral, 

251- 252 

formal solution by perturbation 
method, 250-251 

iteration solution for characteristic 
values and coefficients, 253-254 
properties of indefinite integral, 

252- 253 

Power transmission in standard 
propagation, 31-32 
antenna gain, 31 

general transmission formula, 31-32 
thermal noise power, 32 
Precipitation echoes in radar, 184-185 
Profile method of permanent echo 
prediction, 137-144 
detailed example of difficult site, 
141-144 

estimation of diffraction effects, 
139-140 

general procedure, 140-141 
line-of-sight curve, 138-140 
plotting rules, 141 
principal requirements, 138 
Projects and contracts 
see Contracts and projects 
Propagation, influencing factors 
guided propagation, 190 
refraction, 189-190 
standard refraction, 189-190 
superfraction, 190 
Propagation, nonstandard 
see Nonstandard propagation 
Propagation, standard 
see Standard propagation 
Propagation Committee 
see History of Propagation 
Committee 

Propagation equation solution with 
Hankel functions, 237-239 
conclusions, 239 
exponential decay factor of 
horizontal waves, 237-238 
field of dipole source equation, 237 
given dependence of refraction index 
upon height, 237-238 
Stokes phenomenon, 238 


Propagation fundamentals, 189-198 
equivalent earth radius flat earth 
diagram, 195 

factors influencing propagation, 
189-190 

ground reflection, 190-193 
horizon diffraction, 197-198 
refraction over curved earth, 194-195 
significance of propagation problems, 
189 

Snell’s law of refraction, 194 
Propagation in oceanic surface duct, 
247 

Propagation research 

equipment problems, 26-27 
meteorological problems, 26-27 
organization, 6-7 
origin, 5-8 

propagation problems, 26 
recommendations, 26-27 

Radar, early warning heightfinding, 
106-109 

absolute altitude errors, 107-108 
azimuth errors, 108 
range errors, 108 
relative altitude errors, 108 
tolerances, 106-107 
Radar, ground 

see Ground radar, equipment 
Radar, precipitation echoes, 184-185 
Radar and radio transmission 
relationship, 63-65 
Radar coverage variations, 178-184 
cloud echoes in radar, 184-185 
guided propagation, 180-182 
meteorological factors, 182-284 
refraction of radio waves, 178-180 
summary of radar propagation facts 
185 

Radar cross section, 82-84 
Radar data test flights, 176 
Radar errors due to atmospheric 
refraction, 106-109 
conclusions, 109 
derivation of formulas, 109 
early warning heightfinding radar, 
106-109 

gunlaying (antiaircraft) radar, 
106-107, 109 

refraction index variation, 106 
surface surveillance radar, 108 
Radar forecasting, 80-81 
Radar planning device (RPD), 137-138 
Radar range estimation over open 
ocean, 256-257 

attenuation constant, fractional 
change, 256-257 
duct thickness, 257 
low ducts, 256 



316 


INDEX 


Radar siting 

permanent echoes; see Permanent 
echoes in radar siting 
technical aspects, 114-115 
topography, 115-120 
Radar systems, tactical aspects, 
113-114 

Radar vertical coverage calculations 
see Vertical coverage calculations 
for ground radars 
Radio and radar transmission 
relationship, 63-65 
Radio meteorology, 210-224 

advective ducts, coastal conditions, 
213-214 

ducts over open ocean, 214-215 
dynamic effects, 216-218 
fluctuations in signal strength with 
time, 219-222 
fog, 216 

nocturnal cooling, daily variations, 
215-216 

physical causes of strafication, 
212-213 

scattering and absorption by 
water drops, 222-224 
Snell’s law, 224-225 
subsidence, 216-218 
superrefraction, seasonal and global 
aspects, 218-219 

temperature and moisture gradients, 
210-212 

turbulence, 212-213 
Radio scintillations, 219-220 
Radio wave diffraction 
see Diffraction of radio waves 
Radio wave propagation research 
origin, 5-8 

historical background, 5-6 
pertinent aspects of modern warfare, 
5-6 

plan of investigation, 5-6 
purpose of Committee on 
Propagation, 5 

Radio wave refraction, 178-180 
Rain and hail absorption of 
microwaves, 85-88 
Ray tracing, 44-45 
Rayleigh criterion for roughness of 
ground, 36-37 

Rays in stratified atmosphere, 202-204 
Reflected beam, magnitude of field 
intensity, 190-191 

Reflected wave, divergence factor, 170 
Reflection area, general formula, 
160-162 

Reflection coefficients, 32-34, 167-169 
Reflection from elevated layer, 208 
Reflection from ground, 190-193 
complex cases, 193 
coverage diagrams, 190 


earth gain factor, 192-193 
magnitude of field intensity, 190-191 
simple cases, 191-193 
Reflection from rough surfaces, 123-124 
Reflection from tropospheric layers, 
convergence effects, 258-259 
Refraction, atmospheric 

see Atmospheric stratification and 
refraction; Radar errors due to 
atmospheric refraction 
Refraction of radio waves, 178-180 
Refraction over curved earth, 194-195 
Refractive index 
fog effect, 77, 216 
in nonstandard propagation, 42-44 
M curves, 43 
Snell’s law, 42-43 
temperature inversion, 43-44 
variations, 198-200 
Refractive index measurements, 200 
airborne installations, 52 
captive balloons and kites, 52 
stationary installations on towers, 52 
Remote shielding, 119-120 
Research recommendations, 26-27 
RPD (radar planning device), 137-138 

San Diego transmission experiments, 
68-71, 208 

Scattering and absorption of 
microwaves, 82-90 
absorption by atmospheric gases, 
89-90 

aircraft targets, 83-84 
by water drops, 222-224 
clouds, fog, rain, hail, snow, 85-90 
radar cross section, 82-83 
rain and hail absorption, 85-88 
scattering echo, 88-89 
ship targets, 84-85 
Scattering radar cross section, 82-83 
Scintillations, radio, 219-220 
Shielding as fixed echo control, 137 
Ship radar cross section, 84-85 
aircraft carrier, 85 
battleship, 84 
cruiser, 84 
submarine, 85 

Shoreline diffraction, 158, 162 
Signal measurements for ground radars, 
175-176 

Signal strength fluctuations, 219-222 
blackout, 220 
circuit reliability, 222 
duct fades, 220 
effect of waves on sea, 219 
fading on different wavelengths, 
221-222 
fog, 221 

fronts and thunderstorms, 220-221 


nonoptical path, 221-222 
optical path, 221-222 
scintillations, 219-220 
target modulation, 219 
tidal effects, 219 

Siting and coverage of ground radar 
see Ground radar, siting and coverage 
Snell’s law of refraction 
for curved earth, 42-43, 194-195, 
224-225 

general statement, 194, 224 
rays in stratified atmosphere, 
202-204 

Standard coverage charts, graphical 

method of determination, 93-94 
Standard propagation, 31-41, 179-180, 
185 

atmospheric effects, 180 
coverage diagrams, 179-180 
deviations, 179-180 
electromagnetic field, 38-41 
height factor, 180 

optical properties of earth’s surface 
and atmosphere, 32-38 
power transmission, 31-32 
refraction, 179 
summary, 185 

Standard refraction, 34-36,189-190, 217 
see also Standard propagation 
Straight edge diffraction, 128-129 
Stratification, atmospheric 
see Atmospheric stratification and 
refraction 

Stratification causes, 212-213 
advection, 212 
convection, 212 
frictional turbulence, 212-213 
nocturnal cooling, 212 
subsidence, 212 
temperature inversions, 213 
Stratified atmosphere, rays in, 202-204 
Subsidence 

definition, 76, 183-184, 212 
duct formation, 216-217 
fronts, 217-218 
high pressure areas, 79 
standard propagation, 217 
Superrefraction 

see also Guided propagation 
causes, 185 
definition, 190 
duct, 204-207 

operational applications, 208-210 
Superrefraction, world survey 
Arabian Sea, 79-80, 218 
Atlantic Coast of United States, 

79, 218 

Bay of Bengal, 80, 219 
Mediterranean region, 79-80, 218 
Pacific Ocean, 80, 219 
Western Europe, 79-80, 218 



INDEX 


Surface duct, incipient leakage, 
233-234 

Surface duct attenuation diagrams, 240 
Surface surveillance radar, 108 
azimuth errors, 109 
range errors, 109 
Symbols for use in theory of 

nonstandard propagation, 255 

Tactical aspects of radar systems, 

113-114 

Temperature and humidity in meteoro¬ 
logical measurements, 50 
Temperature and moisture gradients, 
210-212 

Temperature inversions 

coastal and maritime conditions, 

77-78 

conditions for occurrence, 76, 213 
conditions over land, 76-77 
M curves, 43-44 
meteorological factors, 182-184 
Terrain effects on antenna 
pattern, 164-166 
cliff edge diffraction, 166 
land reflection and diffraction, 166 
limited reflecting area, 165 
Terrain reflection characteristics, 
167-169 

Test flights for radar data, 176 
Testing of ground radars, 174-177 
Tidal effects on signal strength, 219 
Topography of siting, 115-120 
azimuth of sun, 116-117 
hour angle, 116 
maps and surveys, 115 
orientation, 116-117 
profiles, 115-116 


visibility problems, 117-120 
Transmission experiments, 

angle-of-arrival, 73-74 
Transmission experiments, Antigua, 
71-73 

duct studies, 71 
equipment employed, 71 
field strength records, 71-73 
M curve measurement, 71-72 
Transmission experiments, British, 
58-60 

Irish Sea experiment, 58-59 
overland path, 59-60 
Transmission experiments, Canada, 67 
Transmission experiments, east coast, 
60-65 

Bell Telephone Laboratories, 60 
Radiation Laboratory (MIT), 60 
RCA Communications, Inc., 60 
relationship between radio and radar 
transmission, 63-65 
results, 60-65 

signal occurrence frequency, 63 
Transmission experiments, southwest, 
68-71, 208 
Arizona desert, 71 
San Diego, 68-71, 208 
Transmission experiments, State 

College of Washington, 65-67 
Trapping, 182-185 
see also Guided propagation 
Tropospheric propagation, 189-210 
atmospheric stratification and 
refraction, 198-210 
propagation fundamentals, 189-198 
Turbulence 

see Stratification causes 
Vertical coverage calculation for 
ground radars, 145-174 


__ 317 

1 

antenna patterns, 162-167 
coefficient of reflection, 167-169 
diagram construction, 146-147 
divergence, 170 
earth curvature effect on lobe 
lengths, 166-167 

flat earth lobe angle calculations, 
147-149 

general lobe angle formula, 152-155 
general lobe formula, 171-174 
lobe angles corrected for standard 
earth curvature, 149-152 
lobe diagrams of medium height 
sites, 158 
lobe lengths, 170 
local terrain effects, 164-166 
low site lobes, 155-156 
modified antenna pattern, 162 
reflection area, general formula, 
160-162 

sea reflection with diffuse land 
reflection, 158-159 
shoreline diffraction, 158, 162 
Visibility problems, 117-120 
diffraction angle, 120 
dip and rise, 118-120 
horizon distance, 117-118 
intervening obstructions, 119 
remote shielding, 119-120 
solution by computation, 119-120 
vertical angles, 120 

Wave picture of guided propagation, 
207-208 

Wave propagation, 121 
see also Nonstandard propagation; 
Standard propagation 
Waveguide theory survey, 47-48 
Wired sonde, 51 



























































































































































































































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